Plaintiffs-Appellants are seven inmates in Connecticut state prison facilities who sued Connecticut Department of Correction officials in their official and individual capacities (collectively, “DOC”), alleging that the 2012 revised Administrative Directive 10.7 (“A.D. 10.7″),1 which limits access by inmates to pictorial sexually explicit materials, violates their First Amendment rights. Plaintiffs also assert that the prison regulation’s exception for material that qualifies as “literary, artistic, educational or scientific in nature” is unconstitutionally vague because it does not provide fair notice as to the scope of the prohibited materials and leads to arbitrary enforcement by DOC officials under a subjective standard. JOSEPH BIANCO, C.J. The United States District Court for the District of Connecticut (Underhill, C.J.) conducted a bench trial over five days, during which the court heard testimony from fifteen witnesses, and then issued its Memorandum of Decision on March 9, 2020, ruling in DOC’s favor on the federal claims. We discern no clear error as to the district court’s factual findings in light of the trial record. We further conclude that the district court, based upon its factual findings, properly held that A.D. 10.7 is reasonably related to legitimate penological objectives — namely, promoting a non-hostile work environment for DOC staff, enhancing the safety and security of DOC facilities, and facilitating the rehabilitation of sex offender inmates — and does not violate the First Amendment. In addition, the district court correctly determined that the regulation, including the exception, is neither unconstitutionally vague on its face, nor unconstitutional as applied to plaintiffs. Accordingly, the judgment of the district court is AFFIRMED. Plaintiffs-Appellants are seven inmates in Connecticut state prison facilities who sued Connecticut Department of Correction officials in their official and individual capacities (collectively, “DOC”), alleging that the 2012 revised Administrative Directive 10.7 (“A.D. 10.7″),1 which limits access by inmates to pictorial sexually explicit materials, violates their First Amendment rights. Plaintiffs also assert that the prison regulation’s exception for material that qualifies as “literary, artistic, educational or scientific in nature” is unconstitutionally vague because it does not provide fair notice as to the scope of the prohibited materials and leads to arbitrary enforcement by DOC officials under a subjective standard. The United States District Court for the District of Connecticut (Underhill, C.J.) conducted a bench trial over five days, during which the court heard testimony from fifteen witnesses, and then issued its Memorandum of Decision on March 9, 2020, ruling in DOC’s favor on the federal claims. In particular, the district court applied the four-factor test set forth by the Supreme Court in Turner v. Safley, 482 U.S. 78 (1987), and held that A.D. 10.7 does not violate the inmates’ First Amendment rights. The district court further found that A.D. 10.7 is not unconstitutionally vague. Judgment was entered for DOC on March 12, 2020, and plaintiffs’ appeal followed.2 We discern no clear error as to the district court’s factual findings in light of the trial record. We further conclude that the district court, based upon its factual findings, properly held that A.D. 10.7 is reasonably related to legitimate penological objectives — namely, promoting a non-hostile work environment for DOC staff, enhancing the safety and security of DOC facilities, and facilitating the rehabilitation of sex offender inmates — and passes constitutional muster under the Turner framework. In addition, the district court correctly determined that the regulation, including the exception, is neither unconstitutionally vague on its face, nor unconstitutional as applied to plaintiffs. Accordingly, we AFFIRM the judgment of the district court. BACKGROUND The following facts are drawn from the district court’s factual findings after the bench trial, which we accept unless clearly erroneous. See Krist v. Kolombos Rest. Inc., 688 F.3d 89, 95 (2d Cir. 2012). I. The Development of A.D. 10.7 Prior to 2012, when A.D. 10.7 came into effect, sexually explicit materials, especially pictorial depictions of nudity and sexual acts, were “ubiquitous” in DOC facilities. Special App’x at 4. Although existing administrative directives prohibited the display by inmates of sexually explicit pictorial depictions, possession of such materials was not strictly prohibited, and they were regularly found hanging on inmates’ cell walls and in their lockers. According to Deputy Commissioner Monica Rinaldi, the widespread possession and display of these materials created a “very sexually charged environment” in DOC facilities. Special App’x at 5. In that environment, acts of public indecency by inmates, such as masturbating in front of (typically female) staff, a practice known as “gunning,” were commonplace and, according to former Warden Anne Cournoyer, contributed to a “very threatening environment” for staff.3 Special App’x at 6. In August 2010, then-DOC Commissioner Leo Arnone ordered a review of DOC’s existing directives regarding inmate possession of sexually explicit materials. He convened a committee of six DOC personnel to consider whether DOC could implement a dual-tiered system to allow inmates to possess pictorial depictions of nudity (“softcore” pornography) but ban possession of depictions of explicit sexual activity (“hardcore” pornography). Over the course of six months, the committee reviewed DOC’s existing policy, which banned certain categories of sexually explicit materials, such as those involving sadomasochism, bestiality, children, and non-consensual sexual activity, but otherwise permitted the possession of sexually explicit material.4 In addition to reviewing DOC’s existing policy, the committee examined policies adopted by other states and the Federal Bureau of Prisons and reviewed case law on this issue from other states and the federal courts. As part of its review, the committee considered two types of partial bans of pictorial depictions of sexually explicit material. The first, as referenced above, would ban hardcore pornography, but allow softcore pornography. The committee rejected this option because its implementation would require subjective standards and ongoing monitoring, which would be difficult to codify into objective criteria and would be both expensive and labor-intensive to implement. The second partial ban the committee considered was a two-tiered approach that would impose different standards for inmates depending upon whether or not they were sex offenders. This two-tiered approach was ultimately rejected because the sex offender inmates and non-sex offender inmates were all housed in the general inmate population, thereby making enforcement almost impossible, particularly given that materials within the prisons are bartered by inmates, and thus sex offender inmates would still be able to obtain them. Accordingly, the committee decided that a total ban of pictorial depictions of sexual activity and nudity (except for a limited Artistic Exception discussed below) was necessary, from a practical standpoint, to achieve DOC’s objectives of (1) enhancing the “safety, security, and order” of prison facilities, (2) supporting the rehabilitation of the inmate population, and (3) “reduc[ing] the exposure of [DOC] staff to displays of sexually explicit materials while in the workplace,” thereby seeking to avoid “a hostile work environment, particularly for female staff.” Joint App’x at 99. The result of the committee’s recommendation was A.D. 10.7, which updates the prior directive’s definition of sexually explicit material to include “[a]ny pictorial depiction of sexual activity or nudity.” Joint App’x at 172. A.D. 10.7 also defines a non-exhaustive list of banned pictorial depictions of sexual activity including: sexual intercourse, including genital-genital, oral-genital, or oral-anal contact, whether between persons of the same sex or opposite sex, with any artificial device, or any digital penetration; bestiality; masturbation; sadistic or masochistic abuse; depiction of bodily functions, including urination, defecation, ejaculation, or expectoration; conduct involving a minor, or someone who appears to be under the age of 18; and sexual activity which appears to be nonconsensual, forceful, threatening or violent. Joint App’x at 179. The regulation further defines “[p]ictorial depictions of nudity” as “the visual depiction or display of genitalia, pubic region, buttock, or female breast at a point below the top of the areola that is not completely and opaquely covered.” Joint App’x at 179. Shortly after the revised regulation came into effect, however, DOC determined that the above-referenced definition of nudity was too restrictive because, for example, magazines such as US Weekly that included photographs of female actors in cocktail dresses were banned under the definition. Therefore, DOC amended A.D. 10.7 to narrow the definition of nudity to “the visual depiction or display of genitalia, pubic region, anus or female breast where the areola is visible and not completely and opaquely covered.” Joint App’x at 187. As relevant here, A.D. 10.7 contains several additional limitations. First, A.D. 10.7 includes what the district court referred to as an “Artistic Exception” whereby material “taken as a whole” that is “literary, artistic, educational or scientific in nature” is excepted from the ban. Joint App’x at 179. Second, the regulation states that a publication may not be rejected “solely because its content is…sexual, or because its content is unpopular or repugnant.” Joint App’x at 178. Third, although broadly banning pictorial depictions of sexual activity, AD 10.7′s prohibition on sexually explicit written material largely mirrors that of the prior version of the directive, banning only written material that “by its nature or content, poses a threat to the security, good order, or discipline of the facility, or facilitates criminal activity.” Joint App’x at 179. More specifically, A.D. 10.7 states that “[a] Unit Administrator or designee shall determine that written sexually explicit material of the following types is to be excluded: 1. sado-masochistic; 2. bestiality; 3. involving minors; or 4. materials depicting sexual activity which involves the use of force or without the consent of one or more parties,” Joint App’x at 179-80, an essentially similar prohibition to the one contained in the prior version of the directive, see Joint App’x at 97. Therefore, as relevant here, under A.D. 10.7, written materials of a sexually-explicit nature outside of these categories can still be possessed by inmates. The regulation was phased in over a one-year period in order to, among other things, allow inmates to dispose of banned materials in their possession, and thus the regulation became effective in June 2012. II. The Implementation of A.D. 10.7 As described below, DOC also implemented a procedure for enforcing A.D. 10.7, which included a review of incoming materials in the mail by DOC officials to determine whether such materials were banned under A.D. 10.7. In practice, the mailroom staff of the prison conducts a first-level review of all incoming publications. If a mailroom staff member reviews a publication and determines it does not violate A.D. 10.7, then it is admitted. However, if upon review, the mailroom staff member believes the incoming publication might run afoul of the regulation, the publication is then set aside for a media review “point person” at the prison to conduct a second-level review. This media review “point person” may admit, reject, or present the publication to the larger Media Review Board (“MRB”), of which the “point person” is a member, for the MRB’s determination. The MRB is a group of about 19 DOC personnel from all DOC facilities with distinct backgrounds — that is, corrections officers, custody supervisors, counselors, treatment officers, support staff, a librarian, and an attorney. The MRB meets twice per month for three-hour sessions and reviews about fifty to one hundred publications per session. With a copy of the text of A.D. 10.7 in front of them for reference, MRB members review the materials to determine if the publication is prohibited under the regulation. If the MRB finds that a publication meets the regulation’s definition of prohibited material, it then considers whether the Artistic Exception applies. At trial, MRB members acknowledged that applying the Artistic Exception could be, at times, difficult Any disagreement between MRB members is put to a simple majority vote, and the MRB then catalogues the outcome of every publication it reviews. Inmates are not left without recourse in the process. A decision to reject a publication by the media review point person or the MRB is appealable, and inmates also may preemptively ask DOC if a publication they are thinking of ordering will be admitted under A.D. 10.7. If a publication is rejected, the inmate receives a notice indicating the reason (although they are not allowed to see the publication). The inmate can first appeal to the MRB chairperson and then, if unsuccessful, to the DOC Commissioner’s designee — usually the prison’s director of security — who conducts an independent review. The director of security makes a final decision and sends a notice to the inmate explaining the reason for rejection or the reason for reversal of the MRB’s initial decision. DOC statistics indicate that approximately 68 percent of initial rejections are upheld. III. Procedural History The seven plaintiffs, who were each convicted of a crime in Connecticut and are serving their respective sentences in a DOC facility, brought lawsuits challenging the constitutionality of A.D. 10.7 under the First Amendment. The district court held a two-day bench trial in the first case, Ortiz v. Arnone, No. 3:11- cv-1793 (SRU), in January 2015. During the post-trial briefing in that case, the district court became aware of the additional cases in the district raising the same constitutional challenge to A.D. 10.7 and consolidated all of the cases under Reynolds v. Arnone, No. 3:13-cv-388 (SRU). The district court also appointed new counsel for plaintiffs and a Second Amended Complaint was filed in the consolidated action. The district court subsequently held a three-day bench trial in April 2019. After consultation with the parties, the district court ordered that all of the exhibits and testimony from the Ortiz bench trial become part of the trial record in this consolidated action. In total, the district court heard testimony from fifteen witnesses — including DOC officials and staff, inmates, and expert witnesses — who testified about the prison environment both before and after the 2012 implementation of A.D. 10.7, the development and implementation of the regulation, and the psychological effect of pornography on inmates. Following the bench trial in this consolidated action, the district court issued a 54-page Memorandum of Decision on March 9, 2020, containing its findings of fact and conclusions of law. More specifically, applying the four-factor test set forth by the Supreme Court in Turner v. Safley, 482 U.S. 78 (1987), the district court concluded that A.D. 10.7 did not violate plaintiffs’ First Amendment rights. The district court further held that A.D. 10.7 was not unconstitutionally vague. Judgment was entered for DOC on March 12, 2020. This appeal followed. DISCUSSION On appeal, plaintiffs contend that the district court erred in concluding that A.D. 10.7 did not violate the First Amendment to the United States Constitution. Specifically, although conceding that the reasonableness of A.D. 10.7 is analyzed under the four-factor test set forth in Turner, plaintiffs argue that the district court did not properly weigh, under the Turner standard, the restriction of inmates’ First Amendment rights against the penological interests asserted by DOC. In addition, plaintiffs assert that the district court incorrectly concluded that the Artistic Exception to A.D. 10.7 was not unconstitutionally vague, either facially or as applied to them. In particular, they argue that the Artistic Exception is a subjective standard that encourages arbitrary decisions by DOC officials charged with applying it. Here, we review the district court’s conclusions of law following a bench trial de novo and its findings of fact for clear error. White v. White Rose Food, Div. of DiGiorgio Corp., 237 F.3d 174, 178 (2d Cir. 2001). As discussed below, we find both of plaintiffs’ constitutional challenges to A.D. 10.7 unpersuasive. In its thorough and well-reasoned decision, the district court properly balanced the competing rights of inmates and the interests of DOC officials under Turner in determining that A.D. 10.7 did not violate plaintiffs’ First Amendment rights, and correctly concluded that the regulation, including the Artistic Exception, was not unconstitutionally vague. I. The First Amendment and Challenges to Prison Regulations In cases involving the constitutional rights of prisoners, we must balance competing principles. As the Supreme Court articulated in Turner, “[p]rison walls do not form a barrier separating prison inmates from the protections of the Constitution.” 482 U.S. at 84. Thus, “‘[w]hen a prison regulation or practice offends a fundamental constitutional guarantee, federal courts will discharge their duty to protect constitutional rights.’” Id. (quoting Procunier v. Martinez, 416 U.S. 396, 405-06 (1974)). On the other hand, “[t]he fact of confinement and the needs of the penal institution impose limitations on constitutional rights, including those derived from the First Amendment, which are implicit in incarceration.” Jones v. North Carolina Prisoners’ Lab. Union, 433 U.S. 119, 125 (1977). “A prison inmate, therefore, retains those First Amendment rights that are not inconsistent with his status as a prisoner or with the legitimate penological objectives of the corrections system.” Giano v. Senkowski, 54 F.3d 1050, 1053 (2d Cir. 1995). In weighing these competing interests, both the Supreme Court and this Court have emphasized that deference should be accorded to decision-making in the corrections system because courts are “ill equipped to deal with the increasingly urgent problems of prison administration and reform” and “[r]unning a prison is an inordinately difficult undertaking that requires expertise, planning, and the commitment of resources, all of which are peculiarly within the province of the legislative and executive branches of government.” Turner, 482 U.S. at 84-85 (internal quotation marks omitted); accord Giano, 54 F.3d at 1053. Moreover, given the doctrine of federalism, the exercise of our judicial restraint is especially important where, as here, the administration of a state penal system is at issue. Giano, 54 F.3d at 1053. Therefore, in Turner, the Supreme Court concluded that the appropriate standard of review is “reasonableness.” 482 U.S. at 89. More specifically, under this deferential standard, “[w]hen a prison regulation impinges on inmates’ constitutional rights, the regulation is valid if it is reasonably related to legitimate penological interests.” Id. The Turner Court articulated a four-factor test for assessing the reasonableness of a prison regulation: (1) whether there is a valid and rational connection between the prison regulation and the legitimate, neutral government rationale offered to justify it; (2) whether the prisoner has an alternative means of exercising the constitutional right; (3) the impact that accommodating the prisoner’s constitutional right would have on corrections staff, other inmates, and the general allocation of prison resources; and (4) whether there are ready alternatives to the prison regulation such that the regulation would be an exaggerated response to prison concerns. Id. at 89-91. Further, the burden of proof “is not on the State to prove the validity of prison regulations but on the prisoner to disprove it.” Overton v. Bazzetta, 539 U.S. 126, 132 (2003). In Giano, applying the Turner standard, we held that New York’s policy of banning inmates from possessing nude photographs of their wives and girlfriends did not violate the First Amendment. 54 F.3d at 1051. In addition, many of our sister Circuits have upheld as reasonable under Turner prison policies similar to the one at issue here, including bans on nude photographs and/or sexually explicit materials, because such bans were based upon one or more legitimate penological interests. See, e.g., Jones v. Salt Lake City, 503 F.3d 1147 (10th Cir. 2007) (upholding a Utah county jail’s ban on sexually explicit materials to protect safety and security of the prison, employees, and other inmates); Mauro v. Arpaio, 188 F.3d 1054 (9th Cir. 1999) (en banc) (upholding a county jail’s ban on sexually explicit materials under rationales of safety and security, inmate rehabilitation, and the promotion of a non-hostile work environment for female employees); Waterman v. Farmer, 183 F.3d 208 (3d Cir. 1999) (upholding a ban on “sexually oriented and obscene materials” in a facility exclusively housing sex offenders); Amatel v. Reno, 156 F.3d 192 (D.C. Cir. 1998) (upholding the federal Bureau of Prison’s regulation banning commercial nude photographs); see also Fauconier v. Clarke, 257 F. Supp. 3d 746 (W.D. Va. 2017), aff’d, 709 F. App’x 174 (4th Cir. 2018) (per curiam) (upholding Virginia’s ban on prisoner access to publications containing nudity or sexually explicit acts), cert. denied, 139 S. Ct. 1353 (2019); Josselyn v. Dennehy, 333 F. App’x 581 (1st Cir. 2009) (per curiam) (upholding Massachusetts’ ban on sexually explicit materials or those that feature nudity to help ensure the safety and security of prisons); Strope v. Collins, 315 F. App’x 57 (10th Cir. 2009) (upholding a Kansas prison regulation banning pictures containing nudity under asserted rationales of reducing harassment of staff and managing the sex offender inmate population); see generally Trapnell v. Riggsby, 622 F.2d 290 (7th Cir. 1980) (upholding, prior to Turner, a federal prison’s ban on non-commercial nude and pornographic photographs due to safety and security concerns).5 II. Analysis of A.D. 10.7 under the Turner Standard Plaintiffs’ primary argument is that the district court misapplied the Supreme Court’s four-factor test as articulated in Turner to the facts of this case. DOC offered the following justifications for A.D. 10.7: (1) ensuring the safety and security of prisons; (2) encouraging the rehabilitation of inmates; and (3) promoting a non-hostile and less offensive work environment for DOC employees. Here, plaintiffs focus on the first Turner factor, but nevertheless assert that all of the Turner factors “confirm that A.D. 10.7 is neither a neutral nor legitimate restriction of inmate’s rights.” Appellants’ Br. at 22. We disagree and hold that the district court correctly concluded, under the Turner factors, that A.D. 10.7 does not violate plaintiffs’ First Amendment rights. A. The First Turner Factor: Rational Relationship to a Legitimate Penological Interest The Supreme Court has explained that “[t]he first Turner factor is multifold” and requires proof that “the governmental objective underlying the regulations at issue is [1] legitimate and [2] neutral, and that [3] the regulations are rationally related to that objective.” Thornburgh v. Abbott, 490 U.S. 401, 414 (1989). As discussed below, A.D. 10.7 is rationally related to several legitimate penological interests — promoting a non-hostile work environment for corrections staff, enhancing the safety and security of DOC facilities, and facilitating the rehabilitation of sex offenders in DOC facilities — and A.D. 10.7 is neutral in its application. We discuss each of these penological interests in turn. Non-Hostile Work Environment. DOC asserts the promotion of a non hostile work environment in DOC facilities as a penological interest in support of A.D. 10.7. The district court found that A.D. 10.7 is “rationally related to enhancing a less offensive and non-hostile work environment.” Special App’x at 41. More specifically, the district court explained that “[i]t is plainly rational to believe that removing sexually explicit pictorial depictions from DOC facilities would improve the hyper-sexualized environment within those facilities.” Special App’x at 41. Plaintiffs characterize the district court’s conclusions as “merely a restatement of the false and moralistic claim that the possession of sexually explicit materials causes bad behavior among men” and contend that “[t]here is no evidence to support this opinion.” Appellants’ Br. at 37. We disagree with plaintiffs and conclude that the record fully supported the district court’s conclusion that A.D. 10.7 is rationally related to the penological objective of seeking to provide a non-hostile work environment for DOC staff. The First Amendment does not confer upon an inmate the right to possess or display pictorial depictions of sexually explicit conduct, such that it creates a hostile work environment for corrections staff. See Mauro, 188 F.3d at 1059 (“[A]lthough no court has addressed whether reducing sexual harassment of prison employees is a legitimate penological interest, there is no doubt that protecting the safety of guards in general is a legitimate interest, and that reducing sexual harassment in particular likewise is legitimate.”). In fact, numerous Circuit courts have held that correctional facilities can be held liable under Title VII of the Civil Rights Act of 1964 for failing to remedy a sexually hostile work environment for its employees created by inmates’ behavior. See Beckford v. Dep’t of Corr., 605 F.3d 951, 958 (11th Cir. 2010) (collecting cases); see also Freitag v. Ayers, 468 F.3d 528, 539 (9th Cir. 2006) (“Nothing in the law suggests that prison officials may ignore sexually hostile conduct and refrain from taking corrective actions that would safeguard the rights of the victims, whether they be guards or inmates.”). As set forth below, there was more than sufficient evidence in the record to support the district court’s conclusion that such a hostile work environment existed in DOC facilities, and that DOC rationally implemented A.D. 10.7 to address this legitimate penological interest. The district court relied upon evidence that, prior to the implementation of A.D. 10.7, sexually explicit materials were found throughout DOC facilities — hanging on the walls and in inmate lockers. For example, Eileen Redden, DOC’s director of sex offender treatment programs in DOC, testified that she “often observed pornographic images…taped on [the] windows [of inmates' cells] facing outward so the female staff was forced to look at them.” Special App’x at 5. Similarly, Commissioner Arnone wrote in 2011 that “sexually explicit pictures are [ ] found inside inmate lockers and displayed in other areas of correctional facilities where staff is exposed to them.” Special App’x at 4. Moreover, Deputy Commissioner Monica Rinaldi testified that the common availability of pornography among inmates created “a very sexually charged environment.” Special App’x at 5. Indeed, even one of the plaintiffs testified that DOC facilities were not a “pleasant environment” for female staff. Deferred App’x (“Def. App’x”) at 98. Moreover, several witnesses described “gunning,” i.e., masturbating in front of female staff, to be a prevalent practice at DOC facilities. The district court recounted testimony from Captain Julie Kunkel who testified that, as a DOC corrections officer in the 1990s, “it was pretty gross being a female” officer and that she “can still hear the sounds of the inmates masturbating when you walked on the tier,” which “happened a lot.” Special App’x at 5-6. Former Warden Anne Cournoyer testified that, while she was touring a unit as a correctional counselor, prisoners “oftentimes…would strip down to be naked and just stand there and wait for [her] to come” to then engage in masturbation in front of her. Def. App’x at 130-31. She emphasized that this created “a very threatening environment” for DOC staff. Def. App’x at 131. Accordingly, DOC characterizes its own facilities prior to 2012 as having been “a horrific, hostile and threatening environment, especially for women working in DOC.” Appellees’ Br. at 6. For their part, plaintiffs do not dispute the evidence regarding the severity of the work environment female staff faced at DOC facilities. See Appellants’ Reply Br. at 13 (“Plaintiffs never doubted or dismissed legitimate concerns that female staff are subjected to harassment in these facilities — including harassment from prisoners and male staff.”). Instead, plaintiffs contend that “the evidence at trial was that a ban on sexually explicit materials was not a rational means of combatting this workplace harassment.” Id. We disagree. Both logic and the trial evidence established that A.D. 10.7 was a rational means of addressing these serious workplace issues. Common sense dictates that, if the possession and display of these sexually explicit pictorial materials by inmates created an offensive and hostile workplace environment for staff, banning such materials is a rational means of rectifying and improving that workplace environment. As we have previously held, “[i]t is rational to censor any materials found to create an intolerable risk of disorder under the conditions of a particular prison at a particular time.” Shakur v. Selsky, 391 F.3d 106, 114 (2d Cir. 2004) (internal quotation marks omitted). Indeed, the evidence at trial provided further support for that rational inference. For instance, following the implementation of A.D. 10.7, DOC employees reported a more respectful workplace environment, including significantly fewer instances of gunning. One DOC official noted that “morale…has improved” among employees following the implementation of the pornography ban under A.D. 10.7. Def. App’x at 29. Similarly, DOC statistics bore out these observations and sentiments of DOC employees, as there was a significant reduction in public indecency tickets issued in DOC facilities after A.D. 10.7 came into effect: from a peak of 494 tickets in 2012 to only 79 tickets in 2018. On appeal, plaintiffs argue that much of the pre-2012 hostile work environment was due to the behavior of male staff, rather than inmates, as evidenced by lawsuits filed by female DOC staff. However, as plaintiffs themselves acknowledge, the lawsuits brought by female staff against male staff alleging sexual harassment were settled in April 2003 — almost ten years before A.D. 10.7 was implemented — and the hostile work environment persisted. Moreover, as noted above, the testimony and other evidence at trial made clear that the hostile work environment observed and reported by DOC staff was attributable to the conduct of inmates, apart from any other issues that may have remained in DOC facilities with regard to harassing conduct committed by staff. Additionally, plaintiffs contend that the committee that devised and recommended A.D. 10.7 did so without consulting either an advisory committee on women’s issues or a working group on sexual harassment, both formed by DOC in response to the prior sexual harassment litigation. However, it is unclear why such consultation would be required when the DOC Commissioner formed a separate committee to focus on sexual harassment and hostility emanating from inmates, including the practice of gunning. There is nothing irrational about DOC seeking to reduce overall hostility in the workplace from both sources by forming separate groups to deal with harassment by male staff and then implementing a regulation to confront and reduce sexual harassment by inmates. Although some consultation between the two committees may have been constructive or prudent, the lack of such consultation does not render A.D. 10.7 irrational. In sum, we conclude under the first Turner factor that A.D. 10.7 is rationally related to the legitimate penological interest of promoting a non-hostile work environment for DOC staff. Safety and Security. Another penological interest asserted by DOC in support of A.D. 10.7 is the safety and security of its prisons. DOC argued, inter alia, that: (1) the bartering of sexually explicit materials often leads to fights between inmates, which would be avoided with the pornography ban; (2) the ban would improve cell shakedowns (i.e., thorough searches of inmates’ cells); and (3) the ban would reduce inmate aggression in DOC facilities. As an initial matter, the district court, relying on “rudimentary supply-and-demand economics,” rejected the DOC’s first justification for the pornography ban based on the avoidance of fights related to the bartering of pornography. Special App’x at 34 (“[T]he underground price of sexually explicit material in DOC facilities has risen since the 2012 ban…[which] makes it much more likely that bartering of sexually explicit materials will cause fights because inmates are more likely to fight over large debts than over small debts.” (emphasis added)). However, the district court held that DOC’s other safety and security rationales provide additional support for the reasonableness of A.D. 10.7 under the first Turner factor. We agree and hold that there is sufficient evidence in the record to support the district court’s conclusions as to these safety and security justifications. As described by a DOC official, prior to the implementation of A.D. 10.7, cell shakedowns, typically conducted by two corrections officers, would reveal contraband items such as “drugs, currency and razors” found “concealed behind or within [] pornographic materials and photographs.” Def. App’x at 460-61. In one instance recounted at trial, a corrections officer described finding “Latin King hand signs” hidden within a Penthouse magazine. Def. App’x at 24. The district court also credited trial testimony from both an inmate and a DOC official that female corrections officers were particularly disinclined to search through pornography while performing cell shakedowns. Def. App’x at 5, 25 (inmate and corrections officer describing how male corrections officers would review sexually explicit materials instead of their female counterparts); accord Def. App’x at 93 (a plaintiff stating that, in his experience, two female officers would not together conduct a cell shakedown). Both below and now on appeal, plaintiffs argue that there is no evidence that cell shakedowns are more effective since the 2012 ban. They also argue that there is no evidence that the presence of sexually explicit materials prevented corrections officers from searching cells or posed a health or safety risk to officers conducting searches. However, we conclude that there is no basis to disturb the district court’s finding that the “presence of sexually explicit materials” made it “more likely that a corrections officer conducting a shakedown w[ould] miss something the officer otherwise might have caught.” Special App’x at 33. There was evidence in the record to support DOC’s view that cell shakedowns became more effective and efficient because officers were, inter alia, more apt to search cells thoroughly when they no longer had to avoid pornographic materials because of “embarrassment,” “disgust,” and concerns for hygiene. Def. App’x at 410-11, 461. Thus, the need to conduct efficacious cell shakedowns in maintaining a safe and secure prison facility supports the reasonableness of A.D. 10.7. We similarly find no error in the district court’s conclusion that “it is reasonable for [DOC] to have believed that the availability of pornographic material would make it easier for predators to sexually assault other inmates.” Special App’x at 36. More specifically, Redden, who oversaw DOC’s sex offender treatment program, including facilitating therapy sessions for DOC inmates, recounted her experience interviewing victims of sexual assault within the prison who described a “pattern” of predatory behavior, whereby predators would offer pornography to their intended victims as a tool of manipulation. Def. App’x at 432. The trial record also contained statements by the United States Department of Justice’s National Institute of Corrections on the subject of inmate sexual assault, averring that prison predators may use pornography “to manipulate other inmates.” Def. App’x at 331. Plaintiffs argued at trial that “lots of guys look at pornography,” and that “doesn’t mean they’re going to rape their cell mate.” Special App’x at 33. However, the question under the Turner test is not whether such violence is common or likely, but rather whether it was rational for DOC to believe that at least some violence in the prison facility could be prevented through the regulation. In other words, although the evidence is far from definitive on the relationship between inmate aggression and the viewing of pornography, DOC was not required to demonstrate “extensive empirical support…before making the common sense determination that these photographs may provoke violence.” Giano, 54 F.3d at 1055. Thus, in Giano, we upheld a prison ban on nude photographs of inmates’ wives, girlfriends, and other loved ones, rejecting the “need for extensive factual ‘proof’ of the link [between the legitimate government interest and the prison's policy]…because we accord substantial deference to the informed judgment of prison officials on matters of prison administration.” Id.; see also Thornburgh, 490 U.S. at 417 (“We agree that it is rational for the Bureau [of Prisons] to exclude materials that, although not necessarily ‘likely’ to lead to violence, are determined by the warden to create an intolerable risk of disorder under the conditions of a particular prison at a particular time.”). Here, according that same “substantial deference to the informed judgment of prison officials” that we articulated in Giano, 54 F.3d at 1055, there was sufficient record evidence to support DOC’s reasonable belief that the pornography ban would improve safety and security in the prison by reducing the amount of inmate-on-inmate sexual violence. Other courts have reached the same conclusion under analogous circumstances. See, e.g., Jones, 503 F.3d at 1155-56 (“The jail’s ban on inmate access to ‘sexually explicit material’ and ‘technical publications’ is expressly aimed at advancing jail security and the ban on ‘sexually explicit material’ also protects the safety of jail personnel and other inmates.”); Trapnell, 622 F.2d at 293 (“The defendants proved, to the satisfaction of the magistrate [judge] in the proceedings below, that the propensity for violence is increased by the possession of such photos. This conclusion is supported by the highly the possession of such photos. This conclusion is supported by the highly emotionally charged nature of the photographs and the assaultive background of [the facility's] inmates.” (internal quotation marks and citation omitted)). In short, A.D. 10.7 is reasonably related to the legitimate penological interest of improving safety and security in the prison not only for DOC staff, but for the inmates themselves. Rehabilitation. The additional penological interest asserted by DOC — that the ban would promote the rehabilitation of inmates — was debated at length in the district court. The debate centered on the rehabilitative effect of the pornography ban as to both sex offender and non-sex offender inmates. After hearing the trial evidence, the district court declined to take a position as to whether “the connection between the 2012 ban is reasonably related to the goal of rehabilitating all inmates,” Special App’x at 40, but concurred with other courts that have found a rational relationship “between bans on sexually explicit materials and the rehabilitative goal of reducing the likelihood that sexual offenders will commit future sex crimes or violence against women,” Special App’x at 38. The district court stated that, “[i]n this case, both record evidence and common sense support that conclusion.” Special App’x at 38. We conclude that there was sufficient evidence in the trial record for the district court to reach this conclusion. Redden, based upon her research and more than 30,000 hours of experience providing programs and treatment to sex offenders, testified that the ubiquitous exposure to pornography in DOC facilities interferes with the rehabilitation efforts of sex offenders. She explained that pornography has negative effects on sex offenders and their rehabilitation because pornography reinforces tendencies to objectify others and to de-sensitize sex offenders to their victims. Citing research by Gert Hald, Neil Malamuth, and Carlin Yuen, Redden testified to a correlation between viewing pornography and “problem” sexual behavior, as well as negative attitudes towards women. Def. App’x at 430-31. Moreover, relying on her own experience talking to sex offenders housed in DOC facilities, Redden further explained, as it related to DOC facilities, that sex offenders “often complained” about the prevalence of pornography in prison because they “could not get away from it.” Def. App’x at 429. Redden further noted that, in addition to sex offender inmates complaining about the prevalence of pornography in their housing units, they would “use pornography as a primary source of meeting emotional, psychological and sexual needs, thereby disabling their ability to relate and create attachments” and that the use of pornography might even “break[] down their ability to view or participate in sexual activities in any healthy way.” Def. App’x at 429. Other courts also have shared the district court’s conclusion that the reasonableness of the pornography regulation is supported not only by this type of psychological evidence, but also by common sense. See generally Amatel, 156 F.3d at 199 (“[T]he regulations restrict prison consumption of publications that implicitly elevate the value of the viewer’s immediate sexual gratification over the values of respect and consideration for others. Common sense tells us that prisoners are more likely to develop the now-missing self-control and respect for others if prevented from poring over pictures that are themselves degrading and disrespectful.”). In response, plaintiffs argued that the national recidivism rate among sex offenders was extremely low, and the rate among formerly incarcerated prisoners in DOC facilities was even lower. Plaintiffs’ expert, Dr. Robert Selverstone, a psychologist and sex educator, countered Redden’s testimony and opined that viewing pornography has generally either neutral or positive effects and helps with “self-soothing, [ ] self-control, [and] stress release.” Def. App’x at 104. He also disputed that there was a negative relationship between the availability of pornography and sex offenders’ negative attitudes towards women. To be sure, as the district court acknowledged, there is no doubt a difference of expert opinion as to whether the viewing of adult pornography interferes with the rehabilitation of sex offenders. However, as discussed above in connection with the safety and security interest, all that Turner requires is that there be a rational connection between the policy and the regulation. As the Ninth Circuit explained in Mauro: The relationship between the jail’s policy of prohibiting the possession of sexually explicit materials and the goals of preventing sexual harassment of the female officers, inmate rehabilitation and maintenance of jail security is not so remote as to render the policy arbitrary or irrational. Although, as the defendants candidly admit, the ‘fit’ between the policy and the jail’s objectives is not ‘exact,’ an exact fit is not required. Rather, all that is required is that there be a ‘rational’ connection between the policy and the jail’s legitimate objectives. This standard is met. 188 F.3d at 1060 (internal quotation marks and citations omitted); accord Amatel, 156 F.3d at 199 (“It does not matter whether we agree with the legislature, only whether we find its judgment rational. The question for us is not whether the regulation in fact advances the government interest, only whether the legislature might reasonably have thought that it would.”). Here, we similarly hold that this modest standard has been met. Indeed, even plaintiffs’ expert, Dr. Selverstone, acknowledged at trial that at least some of the research supported Redden’s experience and testimony that “exposure to pornography…was correlated with negative attitudes toward women.” Def. App’x at 113. Thus, there was sufficient evidence, as found by the district court, to support the conclusion that it was “valid and rational” for DOC to implement a pornography ban to promote the rehabilitation of sex offenders in DOC facilities.6 Giano, 54 F.3d at 1055. In reaching this decision, we recognize that the plaintiffs in this case are not sex offenders and, thus, may question why this rationale should apply at all to their ability to access such materials. Indeed, sex offender inmates could similarly argue that, even though adult pornography affects rehabilitation for some sex offenders, it does not necessarily affect rehabilitation for all sex offenders.7 However, because sex offenders are housed with the general inmate population in DOC facilities, it was reasonable for DOC to conclude, as a practical matter, that it would be impossible to limit access and exposure to pornography to only some inmates, and thus application of A.D. 10.7 to all inmates was a rational means to promote the legitimate penological interest of rehabilitation for, at a minimum, a subset of sex offenders as to whom DOC reasonably believed such materials were harmful. Finally, we emphasize that, even in the absence of DOC’s hotly-debated rehabilitation justification, the other legitimate penological interests asserted by DOC — that is, promoting a non-hostile work environment for DOC staff and ensuring the safety and security of staff and inmates alike — each independently support the constitutionality of A.D. 10.7 under this component of the Turner test. * * * The first Turner factor also requires that the legitimate governmental objective be “neutral.” Turner, 482 U.S. at 90. As the Supreme Court clarified in Thornburgh, Turner does not require the regulation to necessarily be content-neutral; rather, the “reference to ‘neutrality’ in Turner was intended to go no further than [to] require[ ]…that the regulation or practice in question must further an important or substantial governmental interest unrelated to the suppression of expression.” 490 U.S. at 415 (internal quotation marks and citation omitted). Therefore, “[w]here…prison administrators draw distinctions between publications solely on the basis of their potential implications for prison security, the regulations are ‘neutral’ in the technical sense in which [the Supreme Court] meant and used that term in Turner.” Id. at 415-16; see also Hanrahan v. Mohr, 905 F.3d 947, 956 (6th Cir. 2018) (“[T]he ‘technical sense’ of the term ‘neutral’ does not require that a regulation be divorced from the speech’s content — indeed, the [Supreme] Court recognized that the publication regulations upheld in Thornburgh ‘turn[ed], to some extent, on content.’” (quoting Thornburgh, 490 U.S. at 415-16)). Here, A.D. 10.7 furthers substantial penological interests unrelated to the suppression of expression — i.e., protecting DOC staff from a hostile work environment, ensuring the safety and security of DOC facilities, and facilitating the rehabilitation of sex offender inmates. Moreover, A.D. 10.7 draws distinctions between banned sexually explicit pictorial materials that substantially undermine these important penological interests and are therefore banned, as compared to pictorial materials containing sexual content that fall within the Artistic Exception and various categories of written sexually explicit materials that are not prohibited under A.D. 10.7. Therefore, the district court properly concluded that A.D. 10.7 satisfied the “neutrality” requirement in Turner. B. The Second Turner Factor: Alternative Avenues of Expression The second Turner factor assesses whether “there are alternative means of exercising the right that remain open to prison inmates.” Turner, 482 U.S. at 90. In other words, we consider what “other avenues remain available for the exercise of the asserted right.” Id. (internal quotation marks omitted). Here, plaintiffs seek to define the right as “to possess and view pictorial depictions of nudity and sexual activity.” Appellants’ Br. at 38. Thus, they argue, the second Turner factor favors them because A.D. 10.7 prohibits all pictorial pornography. However, we define the right at issue “sensibly and expansively” and “allow for flexibility in determining what qualifies as another means of expression.” Giano, 54 F.3d at 1055 (first quoting Thornburgh, 490 U.S. at 417; then citing Turner, 482 U.S. at 92). Accordingly, we decline to accept the formulation of the right as proposed by plaintiffs and, instead, agree with the district court’s adoption of the broader “right to receive sexually explicit communications.” Special App’x at 44. As noted above, in addition to allowing pictorial materials containing sexual content that are not within the definition of “sexually explicit” or fall within the Artistic Exception, A.D. 10.7 also permits possession by inmates of various categories of written sexually explicit materials. Plaintiffs assert that writings are not the same as pictures for purposes of the First Amendment and that pictorial materials protected by the Artistic Exception or sexually suggestive television shows and commercials (which are not prohibited by A.D. 10.7) are not the same as, for example, a Playboy magazine However, prison officials need not provide alternative means of expression that are identical in nature to the banned modes of expression to withstand a constitutional challenge; rather, courts look to see whether the prison officials allow similar alternative forms of expression that are consistent with the penological interests at stake. For example, in Giano, we upheld a prison regulation banning nude and sexually explicit photographs of wives and girlfriends of inmates under the second Turner factor because inmates could still receive “commercially produced erotica” or “conventional photographs [of loved ones] and romantic letters.” 54 F.3d at 1056; see also Mauro, 188 F.3d at 1061 (defining the relevant right, in evaluating a prison ban on sexually explicit materials including frontal nudity, as “the right to receive sexually explicit communications”). Therefore, although a sexually suggestive television show or a sexually-explicit novel may be an imperfect substitute for a Playboy, just as a romantic letter from a loved one is different from a sexually-explicit photograph of that loved one as analyzed in Giano, the alternatives available in DOC facilities for the receipt of sexually explicit communications, as well as pictorial materials with sexual content that fall under the Artistic Exception or are outside the definition of “sexually explicit,” are sufficient for us to conclude that “‘other avenues’ remain available for the exercise of the asserted right.” Giano, 54 F.3d at 1056 (quoting Turner, 482 U.S. at 90). Thus, A.D. 10.7 satisfies the second Turner factor. C. The Third Turner Factor: Ripple Effect of the Asserted Right The third Turner factor requires us to evaluate “the impact accommodation of the asserted constitutional right will have on guards and other inmates, and on the allocation of prison resources generally.” Turner, 482 U.S. at 90. When “the ripple effect” from the accommodation would be significant, “courts should be particularly deferential to the informed discretion of corrections officials.” Id. (internal quotation marks omitted). The district court concluded that “accommodating the Plaintiffs’ asserted right to receive sexually explicit communications would have a significant ripple effect on fellow inmates and prison staff.” Special App’x at 44. Based upon the district court’s factual findings during the bench trial, which survive clear error review, there was sufficient evidence in the record for the district court to reach this conclusion as to the third Turner factor. As discussed in reference to the first Turner factor, there was substantial evidence that DOC’s pre-A.D. 10.7 policy had resulted in sexually explicit pictorial materials being rampantly displayed and possessed by inmates, which had a “ripple effect” on staff in terms of the work environment, as well as on staff and inmates as it related to safety and security concerns in the prison facilities and the rehabilitation of sex offender inmates. See Amatel, 156 F.3d at 201 (noting that the third Turner factor is “in part a restatement of the deferential balancing called for under the first factor”). In short, we need not resort to a prediction about the ripple effect that may be caused by the inmates’ assertion of the right at issue here — that is, the right to unrestricted access to sexually explicit pictorial materials. Instead, as was demonstrated by the evidence credited by the district court after an extensive bench trial, such a ripple effect on staff and inmates from the assertion of that right had already been experienced and documented for many years within DOC facilities prior to the implementation of A.D. 10.7. There is sufficient evidence in the record that, prior to the implementation of A.D. 10.7 in 2012, the inmate right at issue was being exercised with significant costs to the work environment of DOC staff and with risk to the safety and security of staff and inmates alike, as well as the rehabilitation of sex offender inmates. Under those circumstances, we should defer to the “informed discretion of corrections officials” under the third Turner factor. 482 U.S. at 90. D. The Fourth Turner Factor: The Existence of Obvious, Easy Alternatives The fourth Turner factor considers whether there are easily available alternatives to the regulation. As the Supreme Court explained in Turner, “[t]he existence of obvious, easy alternatives [to the regulation] may be evidence that the regulation is not reasonable, but is an ‘exaggerated response’ to prison concerns.” 482 U.S. at 90. However, the Court emphasized that “[t]his is not a ‘least restrictive alternative’ test” and “prison officials do not have to set up and then shoot down every conceivable alternative method of accommodating.” Id. Instead, “if an inmate claimant can point to an alternative that fully accommodates the prisoner’s rights at de minimis cost to valid penological interests, a court may consider that as evidence that the regulation does not satisfy the reasonable relationship standard.” Id. at 91. As a potential alternative, plaintiffs point to a two-tiered system whereby inmates would be able to possess photographs of nudity (softcore pornography) but not of sexually explicit acts (hardcore pornography). Although Turner does not require DOC to consider every conceivable alternative method of accommodation, this and other alternatives were explicitly considered and rejected by the DOC committee after “[s]ubstantial thought and discussion” (including a review of two-tiered approaches by other states) that led to the conclusion that “any form of a divided policy” was not a viable alternative. Joint App’x at 100. More specifically, as the DOC committee further explained, a partial ban would require “an ongoing monitoring system” with “subjective standards that would be difficult to codify into any kind of a strictly objective criteria.” Joint App’x at 100. As one DOC official and committee member further noted, a partial ban “would, therefore, result in an inconsistent implementation of the policy” and in a system that “would be [both] financially costly and labor intensive.” Def. App’x at 438. After weighing these various practical considerations, the Committee concluded: In the end, it seems prudent to the committee that if we as an agency feel strongly enough about the detrimental effects on our staff and the inmates resulting from the presence of such publications in our correctional facilities, then a total ban makes the most sense, would be the easiest to implement, and would be the most practical. Joint App’x at 101. The burden of proof “is not on the State to prove the validity of prison regulations but on the prisoner to disprove it.” Overton, 539 U.S. at 132. Here, plaintiffs have failed to adequately address the practical obstacles to the implementation of a partial ban and have not demonstrated that any type of partial ban was an “obvious, easy alternative[] to the policy.” Giano, 54 F.3d at 1056. As the district court additionally noted, “[t]he fact that numerous other correctional systems employ similar bans on sexually explicit publications is further evidence that there are no obvious, easy alternatives to the 2012 ban at issue here.” Special App’x at 48. Plaintiffs have similarly failed to demonstrate, through other proposed alternatives or any other proof in the record, that A.D. 10.7 is an “‘exaggerated response’ to prison concerns.” Turner, 482 U.S. at 90. To the contrary, DOC even updated the definition of nudity shortly after implementing A.D. 10.7 when it became clear that the prior definition was unnecessarily restrictive. We are also unpersuaded by plaintiffs’ suggestion that DOC had the viable alternative of increasing the enforcement of prohibitions against, and punishment for, certain infractions such as gunning, that would address all of DOC’s broader legitimate penological goals. Critically, plaintiffs do not explain how such an alternative (even if effective at reducing such infractions) would address the broader penological interests regarding the workplace and the safety and security of the prison, as well as the rehabilitation of sex offender inmates, created by the possession and/or display of these pictorial materials. In short, plaintiffs have failed to “point to an alternative that fully accommodates the prisoner’s rights at de minimis cost to valid penological interests.” Id. at 91. Accordingly, we agree with the district court that the fourth Turner factor also weighs in favor of defendants because plaintiffs have failed to demonstrate that there are any easily available alternatives to A.D. 10.7. In sum, A.D. 10.7 satisfies the reasonableness test set forth in the Turner factors and does not violate plaintiffs’ First Amendment rights. III. The Vagueness Challenge Plaintiffs also separately challenge A.D. 10.7 as being unconstitutionally vague. More specifically, they contend that, even if the regulation satisfies the Turner test as to their First Amendment challenge, it is still unconstitutional because it “encourages arbitrary and erratic behavior on the part of officials charged with enforcing the rule.” Appellants’ Br. at 45 (quoting Giano, 54 F.3d at 1057). As an initial matter, DOC contends that the vagueness test applied to criminal statutes has no application to prison regulations and that, if the regulation satisfies the four-part reasonableness test set forth in Turner, no separate vagueness challenge can prevail. Some Circuit courts have adopted this view. For example, in Waterman v. Farmer, the Third Circuit declined to specifically address the vagueness and overbreadth challenges and, instead, held that “if the challenged statute withstands review under [Turner], it does not violate the Constitution.” 183 F.3d at 213; see also Bahrampour v. Lampert, 356 F.3d 969, 975-76 (9th Cir. 2004) (rejecting claims of vagueness and overbreadth by reference only to the Turner factors). Plaintiffs counter by noting that, in Giano, we separately analyzed a vagueness challenge even after we concluded that the prison regulation regarding nude photographs satisfied the Turner test. 54 F.3d at 1057. That approach is consistent with other decisions by this Court that have specifically considered vagueness challenges to prison regulations. See Farid v. Ellen, 593 F.3d 233, 240 (2d Cir. 2010); Chatin v. Coombe, 186 F.3d 82, 87 (2d Cir. 1999). Importantly, in these decisions, the prison regulation at issue resulted in the inmate receiving a disciplinary infraction. In fact, in Chatin, we noted that we were applying the vagueness standard for criminal statutes to a prison regulation because, inter alia, the regulation “carries penalties which are more akin to criminal rather than civil penalties.” 186 F.3d at 86-87; see also Farid, 593 F.3d at 241 (considering whether rules under which inmate was disciplined were unconstitutionally vague). Here, in contrast, A.D. 10.7 has no disciplinary mechanism and, thus, none of the plaintiffs allege that they have been subject to any disciplinary sanction under A.D. 10.7; rather, plaintiffs allege that they discarded materials prohibited under A.D. 10.7 and DOC will remove any prohibited materials from the incoming mail in its screening process before inmates receive them. Although this important distinction between prison regulations that may result in disciplinary action and those that do not may certainly impact the nature of the vagueness review for a particular prison regulation, it is nevertheless difficult to see how the lack of a disciplinary sanction could render a prison regulation limiting First Amendment activity completely immune from any vagueness challenge. See generally Hills v. Scottsdale Unified Sch. Dist. No. 48, 329 F.3d 1044, 1056 (9th Cir. 2003) (“A policy can be unconstitutionally vague if the standard (or lack thereof) creates the danger of viewpoint discrimination; this is true even if there is no sanction or penalty imposed on the speaker.”). Moreover, although we recognize that there may be some overlap between the inquiry under the Turner test and aspects of a vagueness analysis, see Thornburgh, 490 U.S. at 416-17 (discussing arbitrariness concerns in the context of the four-factor Turner test), it is nonetheless possible to imagine a situation where a prison regulation could be found to withstand a First Amendment challenge under the Turner factors, but still run afoul of the Due Process Clause because one or more of its terms is unconstitutionally vague. See Amatel, 156 F.3d at 203 (“Although [Turner] may well function as an all encompassing free speech test for the circulation of reading materials in prison, supplanting otherwise applicable First Amendment doctrine, it may be that plaintiffs’ vagueness claim has independent force.”). Thus, here, as in Giano, we conduct a separate vagueness analysis apart from the Turner test, and we agree with the district court that plaintiffs’ vagueness challenge to A.D. 10.7 fails on the merits. As the Supreme Court has explained, under the Due Process Clause, “the void-for-vagueness doctrine requires that a penal statute define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” Kolender v. Lawson, 461 U.S. 352, 357 (1983). Therefore, “the challenger can prevail by showing that the statute either ‘fails to provide people of ordinary intelligence a reasonable opportunity to understand what conduct it prohibits’ or ‘authorizes or even encourages arbitrary and discriminatory enforcement.’” Copeland v. Vance, 893 F.3d 101, 110 (2d Cir. 2018) (quoting Hill v. Colorado, 530 U.S. 703, 732 (2000)). However, “[t]he degree of vagueness that the Constitution tolerates — as well as the relative importance of fair notice and fair enforcement — depends in part on the nature of the enactment.” Vill. of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 498 (1982). In other words, “[t]he ‘void for vagueness’ doctrine is chiefly applied to criminal legislation. Laws with civil consequences receive less exacting vagueness scrutiny.” Arriaga v. Mukasey, 521 F.3d 219, 222- 23 (2d Cir. 2008); see also Farid, 593 F.3d at 240 (“The first question we consider is whether, in the special constitutional context of prison regulations, the rules under which [plaintiff] was disciplined were unconstitutionally vague as applied to him.”(emphasis added)); Wolfel v. Morris, 972 F.2d 712, 717 (6th Cir. 1992) (“[T]he degree of specificity required in prison regulations is not the same as that required in other circumstances….”); Meyers v. Aldredge, 492 F.2d 296, 310 (3d Cir. 1974) (“Due process undoubtedly requires certain minimal standards of specificity in prison regulations, but we reject the view that the degree of specificity required of such regulations is as strict in every instance as that required of ordinary criminal sanctions.”). Here, “pictorial sexually explicit material” under A.D. 10.7 is described as a “visual depiction of sexual activity or nudity,” with additional definitions provided as to “sexual activity” and “nudity.” Joint App’x at 179. More specifically, a “pictorial depiction of sexual activity” is defined with reference to an enumerated list of certain types of sexual acts, Joint App’x at 179, and a “pictorial depiction of nudity” is defined as “the visual depiction or display of genitalia, pubic region, anus or female breast where the areola is visible and not completely and opaquely covered,” Joint App’x at 187. Given the clear and specific definitions of both “sexual activity” and “nudity,” there is no doubt that a person of ordinary intelligence would understand which pictorial materials fell within those definitions. Indeed, the “nudity” definition is even more precise than the definition we found was not unconstitutionally vague in Giano. 54 F.3d at 1057. Thus, plaintiffs appear to limit their vagueness challenge to what they argue is a “cryptic and arbitrary Artistic Exception.” Appellants’ Reply Br. at 15. Under the Artistic Exception, DOC officials may allow inmates to have pictorial material that, “taken as a whole,” is “literary, artistic, educational or scientific in nature,” even if it contains sexually explicit depictions. Joint App’x at 179. Some correctional facilities in other jurisdictions with regulations similar to A.D. 10.7 also include an exception for artistic, educational, or medical publications in an effort to allow some alternatives for sexually explicit pictorial materials under the First Amendment that do not jeopardize the safety or security of inmates or staff. See, e.g., 28 C.F.R. §540.72(b)(3) (allowing inmates in federal correctional facilities access to “[p]ublications containing nudity illustrative of medical, educational, or anthropological content”). In fact, as the district court noted, if plaintiffs were successful in their vagueness challenge to an Artistic Exception, the district court could have potentially left in place a total ban with even less First Amendment access to sexually explicit materials by inmates (if such a ban still satisfied the Turner test). Special App’x at 52 (“[I]t would be an odd result to hold that the Artistic Exception was unconstitutionally vague. Because I have already held the 2012 ban constitutional under the [Turner] analysis (and probably would even without the Artistic Exception), the result for the Plaintiffs would be worse if I held for them on this point. In other words, the 2012 ban would become a complete ban on sexually explicit pictorial depictions and nudity, full stop.”); see also Giano, 54 F.3d at 1057 (“Instead of banning all erotica, prison officials have prohibited only the sexually explicit material with the greatest likelihood for causing violence and disorder within the prison system. Their reward for forging a compromise policy that allows prisoners access to some sexually explicit material is this lawsuit. Perhaps it is true, after all, that no good deed goes unpunished.”). Undeterred by the potential practical implications of this limited vagueness challenge to the exception to A.D. 10.7, plaintiffs argue that the Artistic Exception “does not provide adequate notice to the prisoners on what material may or may not be allowed” and “relies on subjective and personalized notions of how to assess the overall quality of a publication.” Appellants’ Br. at 46. We disagree. In the majority of the applications of A.D. 10.7 to “sexually explicit material,” including as applied to the materials possessed by plaintiffs in their prison facilities, it would be clear to the ordinary person whether or not a particular publication could even potentially qualify under the Artistic Exception. When dealing with an exception that centers upon analyzing whether a particular work is artistic in nature, no more specific definition is readily available — and perfect clarity in every situation is unachievable. See U.S. Civ. Serv. Comm’n v. Nat’l Ass’n of Letter Carriers, AFL-CIO, 413 U.S. 548, 578-79 (1973) (“[T]here are limitations in the English language with respect to being both specific and manageably brief, and it seems to us that although the prohibitions may not satisfy those intent on finding fault at any cost, they are set out in terms that the ordinary person exercising ordinary common sense can sufficiently understand and comply with, without sacrifice to the public interest.”); see also Ward v. Rock Against Racism, 491 U.S. 781, 794 (1989) (“[P]erfect clarity and precise guidance have never been required even of regulations that restrict expressive activity.”). Moreover, to the extent that the line for the Artistic Exception may become less clear when considering certain literary, artistic, or other works, such situations do not render this prison regulation unconstitutionally vague where the regulation contains no disciplinary mechanism and where inmates are permitted to submit any publication for pre-clearance review by DOC officials under the Artistic Exception. See Nat’l Ass’n of Letter Carriers, 413 U.S. at 580 (“It is also important in this respect that the [Civil Service] Commission has established a procedure by which an employee in doubt about the validity of a proposed course of conduct may seek and obtain advice from the Commission and thereby remove any doubt there may be as to the meaning of the law, at least insofar as the Commission itself is concerned.”); see also Hoffman Estates, 455 U.S. at 498 (allowing for less stringent vagueness test for an economic regulation because “the regulated enterprise may have the ability to clarify the meaning of the regulation by its own inquiry, or by resort to an administrative process”); Mason v. Florida Bar, 208 F.3d 952, 959 n.4 (11th Cir. 2000) (“[T]he availability of advisory opinions to gauge the application of [the challenged enactment] to specific situations bolsters its validity.”); accord Arnett v. Kennedy, 416 U.S. 134, 160 (1974) (noting it “important in rejecting the respondents’ vagueness contentions” that a governmental entity was “available to counsel employees who seek advice on the interpretation of” the statute and regulations at issue). In short, because any close case under this non-disciplinary regulation can be preemptively submitted to DOC for review before the inmate orders the publication, no inmate is denied the ability to obtain “fair notice of [the] conduct proscribed or required by the regulation.” Giano, 54 F.3d at 1057. We also find plaintiffs’ argument regarding arbitrary enforcement similarly unpersuasive. The district court found that DOC has implemented an extensive, multi-level review process to facilitate fair and consistent enforcement of A.D. 10.7, including the Artistic Exception. As discussed infra, that process includes a first level review of incoming publications by the prison mailroom staff, a second-level review by a media review point person at the prison, and then a review by the MRB (consisting of a group of about nineteen DOC personnel from all DOC facilities with varied backgrounds, including corrections officers, custody supervisors, counselors, treatment officers, support staff, a librarian, and an attorney). Furthermore, MRB decisions are appealable by the inmate to the MRB chairperson and then to the DOC Commissioner’s designee, usually the prison’s director of security. These multiple layers of review, as well as the appeals process, do not “encourage[] arbitrary and erratic behavior on the part of officials charged with enforcing the rule.” Giano, 54 F.3d at 1057. Nor is the robust process of implementing AD. 10.7 and applying the Artistic Exception indicative, as plaintiffs suggest, of one person’s “individual tastes” or “whether one sees the work as having artistic merit.” Farrell v. Burke, 449 F.3d 470, 489 & n.7 (2d Cir. 2006). Plaintiffs point to the number of MRB decisions overturned on appeal as evidence of arbitrary enforcement, but “what may appear to be inconsistent results are not necessarily signs of arbitrariness or irrationality.” Thornburgh, 490 U.S. at 417 n.15. Instead, the overturning of many of the MRB decisions to reject materials is consistent with the design of the multi-level process, highly focused on producing more uniform results. In Thornburgh, the Supreme Court rejected a facial challenge to regulations that permitted a prison warden to reject incoming publications under certain circumstances, emphasizing that “[w]here the regulations at issue concern the entry of materials into the prison, we agree with the District Court that a regulation which gives prison authorities broad discretion is appropriate.” Id. at 416. Although plaintiffs argue that Thornburgh is inapposite because it did not, as here, specifically address a vagueness challenge, its analysis of arbitrariness, as it relates to a prison regulation prohibiting certain materials from entering the facility, certainly provides helpful guidance in determining what level of subjective discretion or inconsistency can be constitutionally tolerated under a vagueness challenge to a prison regulation of this nature. Therefore, although MRB members described how applying the Artistic Exception could be, at times, difficult or subjective, and could produce disagreements among MRB members, we bear in mind the Supreme Court’s caution in Thornburgh that “greater consistency might be attainable only at the cost of a more broadly restrictive rule against admission of incoming publications.” Id. at 417 n.15. Moreover, as the Supreme Court noted that it was “comforted by the individualized nature of the determinations required by the regulation,” id. at 416, so, too, are we comforted in this case by the individualized and extensive review process for materials under A.D. 10.7. That process and its implementation, in out view, is sufficiently robust to survive any separate vagueness challenge based upon arbitrary enforcement. Accordingly, we conclude that A.D. 10.7, including the Artistic Exception, is not unconstitutionally vague on its face, or as applied to plaintiffs. CONCLUSION We have considered plaintiffs’ remaining arguments and find them to be without merit. Therefore, for the reasons set forth above, we AFFIRM the judgment of the district court. Dated: February 3, 2022