Before DENNIS, HIGGINSON, and WILLETT, Circuit Judges. JAMES L. DENNIS, Circuit Judge: Steven Topletz lost a civil case in Texas state court, and the victorious plaintiff served him with a number of discovery requests aimed at uncovering his assets and sources of income in order to collect on the judgment. Topletz supplied many of the requested records, but he failed to produce documents related to a family trust of which he is a beneficiary. The Texas state court ordered production, but the trustee—Topletz’s brother—purportedly refused to provide Topletz with several of the trust documents. Instead, the trustee sent a letter to Topletz stating that the trust agreement allowed Topletz only to inspect the documents, not to obtain copies of them, and that it would thus breach the trustee’s fiduciary duty to supply Topletz with the requested records. The state court granted a motion for contempt and sanctions against Topletz, finding that the trust agreement did in fact grant him the right to obtain the requested documents and that they were thus under his control for purposes of discovery. The court sentenced Topletz to detention for fourteen days or “until [he] has fully purged himself of this contempt by serving on [opposing counsel] full and/or proper responses and/or documentation.” After his attempts at overturning the decision in state court failed, Topletz filed a habeas petition in federal district court, arguing that the contempt order violated his constitutional right to due process by requiring him to produce documents that he could not obtain. He requested a preliminary injunction to allow him to remain free during the adjudication of his petition. The district court denied Topletz the preliminary injunction because it found that he was unlikely to succeed on the merits of his habeas claim, and Topletz now appeals. Because we agree that Topletz has failed to show a substantial likelihood that the state court’s decision was contrary to clearly established Supreme Court precedent or based on an unreasonable interpretation of the facts in light of the evidence, we AFFIRM. Background and Procedural History The Original Proceeding In 2015, the 416th District Court in Collin County, Texas, found Appellant Steven Topletz liable to Lynda Willis and awarded Willis damages of approximately $1.1 million.[1] A year later, Willis served a series of post-judgment discovery requests on Topletz, seeking to discover his assets and sources of income. While the requests were pending, Willis passed away, and an independent administrator, Raygan Wadle, was appointed to manage her estate. In 2019, Wadle entered an appearance in the civil case and filed a motion to compel production of the records Willis had requested. Topletz produced many documents responsive to the requests, but he failed to supply, inter alia, documents related to the Steven K. Topletz 2011 Family Trust, a trust fund of which he is a beneficiary. Topletz asserted that a confidentiality agreement prevented him from producing the documents. In an April 18, 2017 email exchange with opposing counsel, Topletz’s lawyer at the time appeared to acknowledge that Topletz had access to at least the trust’s tax returns[2] and the trust formation agreement and stated that he would produce these if the court ordered it so long as it also entered a protective order guarding against their disclosure: As I have said, we will produce the tax returns and the Steven Topletz 2011 Family Trust[3] subject to the protective order which I have previously signed and sent to you for entry by the Court when you send me a signed copy of the protective order. I also require an Order from the Court ordering the production of the trust document subject to the protective order so we eliminate the issue of Mr. Topletz being required to breach a contractual agreement without an order of the Court. The court issued the requested protective order, but during a subsequent hearing on the motion to compel, Topletz argued that he should not be required to produce the documents. Citing In re Kuntz, 124 S.W.3d 179, 184 (Tex. 2003), Topletz contended that his simply having access to the documents did not mean that they were in his “possession, custody, or control” as would make them subject to discovery under Texas Rule of Civil Procedure 192.7(b). He argued that Wadle must instead attempt to get the documents directly from the trust. The court ordered the parties to discuss the matter off the record, and, according to statements by the court at a later hearing, Topletz’s counsel agreed to produce the trust’s tax returns during the off-the-record conversation. On June 25, 2018, the court entered an order granting Wadle’s motion to compel, requiring Topletz to produce the trust formation agreement for the court’s in-camera review. If, based on the court’s review, it determined that the trust was not “excused from production by applicable case law,” the order continued, Topletz would be required to produce the trust and any documents responsive to Wadle’s discovery request. Interlined beneath the judge’s signature were the additional sentences: “**Defendant shall produce the trust documents and the tax returns as requested. Defendant shall also produce the other documents requested that are in his possession, custody or control.” Following the order, Topletz sent a letter to Topletz’s brother, who was one of the three trustees managing the trust,[4] and Topletz’s lawyer sent a letter to his brother’s counsel. The letters included copies of the court’s production order and Willis’s original document request, and they requested copies of all responsive documents from the trust. An attorney for Topletz’s brother sent a letter in response that denied the requests, asserting that, “[a]lthough the various beneficiaries may review or examine [the financial] books during ordinary business hours, the terms of the Family Trust stop there” and do not allow beneficiaries to “duplicate, convert, or otherwise receive possession of any such information.” “Transferring possession of such property by the Family Trust’s fiduciary to you and others would constitute a direct breach of the fiduciary duty itself,” the letter stated. The letter, however, concluded by advising that Topletz could submit a request for a profit and loss statement or balance sheet, in which case he would be provided with those documents on or before September 30, 2018. Topletz turned over to Wadle his personal tax returns, the trust formation agreement, and some other unidentified trust-related documents, as well as the letter from the trust denying his request. He then certified to the court that he had produced all responsive documents in his possession, custody, and control. Wadle then filed a motion for contempt and sanctions against Topletz for his failure to produce all of the requested documents related to the trust. Following a series of hearings,[5] the court granted the motion and entered a contempt judgment against Topletz on March 18, 2019. In its order, the court found that Topletz had been ordered to produce but failed to turn over the following specific documents related to the trust: Ownership certificates for all of the stock held by the trust for the previous five years; All of the leases or contracts the trust had entered into since 2012; The trust’s financial statements, including balance sheets and profit and loss reports since 2012; A record of the trust’s accounts receivable showing amounts owed to the trust; Ownership documents for any company owned by the trust; and The trust’s tax returns. These records were “freely available” to Topletz pursuant to paragraph 4.12 of the trust agreement, the court continued, which states Each beneficiary who has attained the age of twenty-five years shall have free access to those books, records and accounts at all reasonable times during regular business hours. If such beneficiary requests, a profit and loss statement, fully disclosing the fiscal operations of the trust for the preceding year, and a balance sheet, which accurately reflects the financial status of the trust at the expiration of the preceding year, shall be furnished to such beneficiary within ninety days of the end of the fiscal year. Any beneficiary who has attained the age of twenty-five years may cause the books, records and accounts of any trust in which the beneficiary has a beneficial interest to be audited at any time. . . . No restriction in the agreement prevented Topletz from “obtaining possession of or copying documents,” the court continued, and the records were therefore “subject to [his] control” for purposes of discovery. The court thus found that Topletz had refused to comply with the court’s production order “without substantial justification.” The court also characterized Topletz’s refusal as contrary to his previous agreement to supply the documents. It thus held Topletz in contempt and ordered that he be taken into custody “until [he] has fully purged himself of this contempt by serving on [Wadle's counsel] full and/or proper responses and/or documentation” to Wadle’s requests, but not for a period “in excess of 6 months.” Notwithstanding the 6-months language in its contempt judgment, the court then signed a commitment order instructing law enforcement to confine Topletz for 14 days, from March 18, 2019 to April 1, 2019, or until he purged the contempt.[6] The State Habeas Petitions The same day the state trial court entered the contempt judgment, Topletz filed a petition for a writ of habeas corpus with the Court of Appeals for the Fifth District of Texas.[7] Again citing Kuntz, Topletz argued that the trial court’s contempt order was void because he did not have possession, control, or custody of the requested documents and he therefore could not purge the contempt. The following day, the appeals court ordered Topletz released while it reviewed his petition. However, six months later the court issued a memorandum opinion denying Topletz’s petition. The appeals court rejected Topletz’s comparison to Kuntz, which concerned a post-judgment discovery request served on the CEO of an oil consulting company for “recommendation letters” that contained evaluations of oil and gas prospects. See In re Topletz, No. 5-19-00327-CV, 2019 WL 4302254 at *4 (Tex. App. Sept. 11, 2019) (citing Kuntz, 124 S.W.3d 179, 182 (Tex. 2003)). The consulting agreement between the CEO’s employer and the oil companies it advised specified that the letters were the property of the oil companies and could not be disclosed to third parties without the oil companies’ consent. Kuntz, 124 S.W.3d at 182. In holding that the letters were not in the CEO’s possession, custody, or control, the Texas Supreme Court specifically relied upon the fact that producing the documents would violate the consulting agreement and subject the CEO to personal liability. Id. at 184. The Texas appeals court held that no similar agreement limited Topletz’s right to produce the requested documents. Topletz, 2019 WL 4302254 at *4. Quoting GTE Communications Systems Corp. v. Tanner, 856 S.W.2d 725, 729 (Tex. 1993), the court stated that, for purposes of the Texas civil discovery rule, “possession, custody, or control” includes not only actual physical possession, but also constructive possession, and the right to obtain possession from a third party, such as an agent or representative. The right to obtain possession is a legal right based upon the relationship between the party from whom a document is sought and the person who has actual possession of it. Topletz, 2019 WL 4302254 at *4. The court held that Topletz had the legal right to access the documents from the trustee, whom it described as Topletz’s agent,[8] and that there existed “no contractual impediment to production” of the documents. Id. The court accordingly held that Topletz had “constructive possession of the trust’s financial documents and tax returns[,] as was recognized by his former counsel who agreed to produce the documents.” Id. The state trial court was entitled to find Topletz’s assertion that he had tried and failed to obtain the documents not credible in light of his counsel’s purported earlier agreement to produce them, the appeals court concluded, and thus it was not clear error for the trial court to find that Topletz had defied the production order and committed contemptuous conduct. Id. Topletz then filed an emergency motion for rehearing with the Court of Appeals for the Fifth District of Texas and a second habeas petition with the Texas Supreme Court. Topletz argued in both filings that, under Texas law, the contempt order was void because it required him to rely on the actions of a third party to purge the contempt. The appeals court and the Texas Supreme Court summarily denied without opinion Topletz’s rehearing motion and second habeas petition, respectively. Following the denials, the state trial court issued a capias[9] for Topletz’s arrest and amended its commitment order to mandate confinement for 14 days following his arrest. The Federal Habeas Petition On November 12, 2019, Topletz filed the federal habeas corpus petition that is the subject of the present appeal. In the petition, Topletz contends that the contempt judgment denied him his federal constitutional right to due process for two interrelated reasons. First, because the Supreme Court has held that civil contempt is inherently a conditional penalty that may only be validly applied to “compel the doing of some act,” Hicks ex rel. Feiock v. Feiock, 485 U.S. 624, 633 (1988), Topletz argues that “[d]ue process requires a civil contempt order to condition a contemnor’s release upon an act the contemnor alone can perform.” Because the requested documents are in the hands of the trustee and producing them requires some action on the trustee’s part, Topletz contends that the contempt order is unconstitutional. Second, Topletz argues that, even if it does not per se violate due process to hold a litigant in contempt for failing to acquire documents from third parties, the state trial court’s determination that Topletz could acquire the specific documents at issue was based on insufficient evidence. He contends that a civil contempt finding must be proven by clear and convincing evidence, a standard that the state court did not explicitly cite. And Topletz argues that the only evidence before the trial court demonstrated that he had tried and failed to obtain the documents. Topletz accordingly argues that it was irrational for the trial court to conclude by clear and convincing evidence that it was possible for him to obtain the documents. Because it violates due process for a state court to imprison a defendant when the evidence is insufficient for a rational trier of fact to find the defendant guilty, Jackson v. Virginia, 443 U.S. 307, 323 (1979), Topletz argues that a habeas corpus writ should issue. On November 19, 2019, Topletz moved for a temporary restraining order and preliminary injunction, asking the district court to enjoin Sheriff Jim Skinner from arresting or holding him pursuant to the contempt judgment. The Sheriff did not oppose a temporary restraining order, and one issued on December 5, 2019. Following a hearing, however, a magistrate judge issued a report recommending that Topletz be denied a preliminary injunction. The magistrate judge found that Topletz was unlikely to succeed on the merits of his habeas claim because both his contentions were likely to fail. First, the magistrate agreed that due process prohibits imprisoning an individual for civil contempt when the contemnor is incapable of purging the contempt. The magistrate found, however, that because the contempt order allowed Topletz to produce “full and/or proper responses [to] and/or documentation [of]” the trust documents, it permitted Topletz to purge the contempt through means other than producing the trust documents themselves. According to the magistrate, Topletz could purge the contempt by providing evidence of his genuine effort to obtain the documents, filing suit against the trust, or providing a summary of information he gained through his personal review of the documents. Because Topletz introduced no evidence that he was unable to purge contempt through these alternative avenues, the magistrate judge concluded, he had failed to show a substantial likelihood that he would succeed on his first argument. As to Topletz’s second challenge, the magistrate stated that, in a habeas proceeding challenging a state judgment, 28 U.S.C. § 2254(e)(1) provides that a state court’s factual findings are presumed correct and a petitioner has the burden of rebutting them by clear and convincing evidence. The magistrate found that, in light of Topletz’s prior counsel’s purported agreement to provide the documents, Topletz had failed to rebut the presumption that the state court was correct that he could produce them. Similarly, the magistrate found that Topletz offered no analysis as to why the evidence on which the state court relied failed to rise to the clear and convincing evidence standard, and he therefore failed to show that the state court employed the incorrect standard. Accordingly, the magistrate found that Topletz was unlikely to prevail on this ground. Finally, the magistrate judge found that, given the small likelihood that Topletz would prevail on the merits, the public interest in ensuring judgment creditors are able to discover judgment debtors’ finances that would be served by denying an injunction outweighed any public interest in avoiding the imprisonment of innocent people that would be served by issuing an injunction. The magistrate judge thus concluded that the public interest weighed in favor of denying a preliminary injunction and recommended that Topletz’s motion be denied. On January 27, 2020, the district court overruled Topletz’s objections and adopted the magistrate judge’s recommended findings and conclusions, denying Topletz’s motion for a preliminary injunction. Topletz filed a timely notice of appeal.[10] Standard of Review This court reviews the grant or denial of a preliminary injunction for abuse of discretion, with any underlying legal determinations reviewed de novo and factual findings for clear error. Dennis Melancon, Inc. v. City of New Orleans, 703 F.3d 262, 267 (5th Cir. 2012). Discussion To obtain a preliminary injunction, Topletz was required to show a substantial likelihood that his habeas petition will be granted on the merits, irreparable injury in the absence of a preliminary injunction, a balance of hardships favoring the issuance of the injunction, and no adverse effect on the public interest. See Melancon, 703 F.3d at 268. When a habeas petition challenges a petitioner’s incarceration pursuant to a state court judgment, 28 U.S.C. § 2254, which was enacted as part of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), limits the scope of federal review. See, e.g., Williams v. Taylor, 529 U.S. 362, 376–77 (2000). As an initial matter, Topletz argues that courts in this circuit are divided as to whether a habeas petition challenging a contempt order should be brought under § 2241, which authorizes habeas relief generally, or § 2254, which contains the AEDPA limitations. However, our caselaw makes clear that the two statutes do not represent an either/or dichotomy. “[Section] 2241 empowers a federal court to grant writs of habeas corpus while § 2254 applies to a subset of those to whom § 2241(c)(3) applies,” mandating the deferential AEDPA standard of review specifically when “a person is in custody pursuant to the judgment of a State court.” Hartfield v. Osborne, 808 F.3d 1066, 1073 (5th Cir. 2015) (quoting Medberry v. Crosby, 351 F.3d 1049, 1059 (11th Cir.2003)) (cleaned up). In other words, “§ 2254 is not an independent avenue through which petitioners may pursue habeas relief.” Id. Instead, all habeas petitions (as distinguished from the § 2255 habeas motions available to prisoners held pursuant to a federal court conviction) are brought under § 2241, and § 2254 places additional limits on a federal court’s ability to grant relief if the petitioner is being held in custody “pursuant to the judgment of a State court.” 28 U.S.C. § 2254(a). As to whether § 2254 applies here, a person who is incarcerated pursuant to a state court’s contempt judgment is, according to the ordinary meaning of the terms, in custody pursuant to the judgment of a state court. Indeed, the Supreme Court has expressly stated as much in dictum. See Duncan v. Walker, 533 U.S. 167, 176 (2001) (“Incarceration pursuant to a state criminal conviction may be by far the most common and most familiar basis for satisfaction of the ‘in custody’ requirement in § 2254 cases. But there are other types of state court judgments pursuant to which a person may be held in custody within the meaning of the federal habeas statute. For example, federal habeas corpus review may be available to challenge the legality of a state court order of civil commitment or a state court order of civil contempt.”). And while our court does not appear to have addressed the matter directly, at least one of our sister circuits has held that AEDPA applies to a state contemnor who seeks federal habeas relief. See Chadwick v. Janecka, 312 F.3d 597, 606 (3d Cir. 2002) (Alito, J.) (applying the AEDPA review limitations contained in § 2254 to state civil contemnor’s federal habeas petition). Thus, the AEDPA standard applies to Topletz’s federal habeas petition. Under AEDPA, if an adequate state “corrective process” for raising a claim exists that the petitioner could avail him or herself of, a federal court may only consider the claim if the petitioner has exhausted available state remedies. 28 U.S.C. § 2254(b)(1). And when the petitioner has done so and the state court has rejected the claim on the merits, federal courts may provide relief only when the state court adjudication was either “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States,” or “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” Id. § 2254(d). The petitioner has the burden of rebutting the presumption that the state court’s determinations of fact are correct by clear and convincing evidence. Id. § 2254(e)(1). Topletz contends that he is entitled to a preliminary injunction because the contempt order against him likely violates his right to due process as protected by the Fourteenth Amendment. The constitutional protections due a contemnor differ depending on whether the contempt is civil or criminal in nature, with criminal proceedings necessitating significantly greater procedural protections. See Turner v. Rogers, 564 U.S. 431, 441–43 (2011). Though this court has in the past stated that whether contempt is civil or criminal turns on “the apparent purpose of the trial court in issuing the contempt judgment,” Port v. Heard, 764 F.2d 423, 426 (5th Cir. 1985) (quoting In re Hunt, 754 F.2d 1290, 1293 (5th Cir. 1985)), the Supreme Court has more recently disavowed such an analysis, see Feiock, 485 U.S. at 635 (“[T]he Court has eschewed any alternative formulation that would make the classification of the relief imposed in a State’s proceedings turn simply on what their underlying purposes are perceived to be.”). Instead, the Supreme Court has held that “the purposes for which relief is imposed are properly drawn from an examination of the character of the relief itself.” Id. at 636. “If the relief provided is a sentence of imprisonment,[11] it is [civil] if the defendant stands committed unless and until he performs the affirmative act required by the court’s order, and is [criminal] if the sentence is limited to imprisonment for a definite period.” Id. at 632 (internal quotations omitted). “Imprisonment for a fixed term similarly is coercive,” and thus civil, “when the contemnor is given the option of earlier release if he complies.” Int’l Union, United Mine Workers of Am. v. Bagwell, 512 U.S. 821, 828 (1994). There are some indications in the record that the state court’s contempt order was intended to be punitive, motivated at least in part by a desire to punish Topletz’s past noncompliance rather than to secure his future compliance.[12] Nevertheless, the state court’s commitment order permits Topletz to secure his release by “purg[ing] himself of the contempt by producing the documents previously ordered.” Because Topletz’s sentence is conditional, we evaluate it as a civil contempt order for which the full panoply of constitutional due process rights afforded to a criminal defendant do not apply. See Feiock, 485 U.S. at 636–37; Turner, 564 U.S. at 441. Topletz Has Not Demonstrated that It Clearly Violates Due Process to Use Civil Contempt to Compel the Production of Items Held by a Third-Party that the Contemnor Has a Legal Right to Obtain. Topletz first argues that using civil contempt to compel an individual to produce documents that are in another party’s actual possession is a per se violation of due process because the ability to purge the civil contempt is not within the contemnor’s sole control. The Due Process Clause of the Fourteenth Amendment provides fewer protections to a civil contemnor than a criminal contemnor. See Turner, 564 U.S. at 441; Feiock, 485 U.S. at 635. As the Supreme Court has explained, it is specifically “[t]he conditional nature of the imprisonment” for civil contempt, which is “based entirely upon the contemnor’s continued defiance,” that “justifies holding civil contempt proceedings absent the safeguards” of criminal due process like “indictment and jury.” Shillitani v. United States, 384 U.S. 364, 370–71 (1966). Therefore, “the justification for coercive imprisonment as applied to civil contempt depends upon the ability of the contemnor to comply with the court’s order.” Id. at 371 (citing Maggio v. Zeitz, 333 U.S. 56, 76 (1948)). And when that rationale does not exist because the contemnor “has no . . . opportunity to purge himself of contempt,” confinement of a civil contemnor violates due process. Id. Under the oft-repeated aphorism, civil contemnors must “carry ‘the keys of their prison in their own pockets.’” Id. at 368 (quoting In re Nevitt, 117 F. 448, 461 (8th Cir. 1902)). Topletz contends that the state court’s contempt judgment violates this principle because he must rely on the trustee’s cooperation to produce the documents needed to purge his contempt, and thus the trustee “holds the keys” to his prison. Topletz’s argument falls short of the high bar set by AEDPA, which requires him to show that the state court’s adjudication of this issue[13] was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). The only Supreme Court case that Topletz cites in which the Court actually addressed the limits the Constitution places on a civil contempt order’s release conditions is Shillitani v. United States, 384 U.S. at 371–72.[14] In Shillitani, the Supreme Court held that, after a grand jury proceeding had concluded, it violated due process to continue to hold two civil contemnors who had been jailed for refusing to testify before the grand jury. Id. at 371–72. “Once the grand jury ceases to function,” the Court reasoned, “the rationale for civil contempt vanishes, and the contemnor has to be released.” Id. at 372. Thus, the “Federal law” on the issue that is “clearly established . . . by the Supreme Court of the United States” is at most that a civil contempt order violates due process if and when it becomes actually impossible for a contemnor to purge the contempt. There is no clearly established Supreme Court precedent that a civil contempt order’s release condition may never require the cooperation of a third party for its fulfillment. Unless the third party’s refusal to cooperate makes the contemnor’s complying with the order actually impossible, Shillitani has nothing to say about the matter. Moreover, Topletz’s claim that he must rely on the trustee’s voluntary cooperation to obtain the requested documents is simply not true. The Texas state trial court and the Court of Appeals for the Fifth District of Texas both concluded that, under Texas law, the terms of the trust agreement give Topletz a legal right to acquire the requested documents. Sheriff Skinner asserts that the trustee’s refusal to provide the documents was not the result of a genuine unwillingness to cooperate, but rather a scheme between the trustee and Topletz to hide Topletz’s assets in order to frustrate a judgment creditor. But even if the trustee’s refusal is genuine, Topletz has legal recourse and can file suit to compel the trustee to give him the documents that he has a legal right to obtain. A rule that due process does not permit the use of civil contempt to compel the production of documents that are in the hands of third parties would also overturn longstanding precedents and would likely be unworkable in practice. Since at least 1993, Texas courts have held that possession of a tangible item such that it is subject to discovery under the state’s rules of civil procedure “includes not only actual physical possession, but constructive possession, and the right to obtain possession from a third party, such as an agent or representative.” GTE Commc’ns Sys. Corp., 856 S.W.2d at 729. And the current Texas Rules of Civil Procedure explicitly state that “[p]ossession, [c]ustody, or [c]ontrol of an item means that the person either has physical possession of the item or has a right to possession of the item that is equal or superior to the person who has physical possession of the item.” TEX. R. CIV. P. 192.7(b) (emphasis added). Depriving courts of the right to use civil contempt to compel production of items subject to this rule would render them impotent to enforce it, thereby allowing a party to evade discovery simply by storing records with a third party. It is also notable that no court has held that the plain language of Texas’s rule violates federal due process; indeed, longstanding decisions of the U.S. Supreme Court suggest the opposite. See, e.g., Oriel v. Russell, 278 U.S. 358, 361 (1929) (affirming federal civil contempt order based on noncompliance with production order where the trial court had “found that the books of account were with the bankrupts or under their control” (emphasis added)). Nor is it an answer that the court could likely order production of the documents directly from the trust pursuant to Texas’s rule for nonparty discovery. See In re Kuntz, 124 S.W.3d at 184 n. 4 (citing TEX. R. CIV. P. 205). That Texas provides litigants and its courts with an alternative avenue for obtaining documents does not bear on whether the method at issue here— compelling a litigant to produce the records through civil contempt—violates due process. The question presented turns solely on whether it is possible for Topletz to purge the contempt, and not whether the contempt was the only possible avenue of achieving the Texas court’s goal. See Shillitani, 384 U.S. at 371–72. The district court below relied heavily on what the parties refer to as the contempt order’s “safety valve” in holding that its release condition did not violate due process. Because the contempt judgment permits Topletz to enter “full and/or proper responses [to] and/or documentation [of]” the requested documents, the court concluded that Topletz could purge the contempt even if it is not possible for him to obtain the documents by, for example, providing evidence of his genuine effort to obtain the documents or summarizing the information that he gained through his review of the documents. While the contempt judgment may well allow Topletz to purge the contempt by methods other than supplying the documents, its validity is not dependent on the order containing such a safety valve. As discussed in more detail infra, an inability to comply with the court’s order is always an affirmative defense to contempt under Texas law. See Ex parte Chambers, 898 S.W.2d 257, 261 (Tex. 1995) (“Although the inability to comply defense technically rebuts the willfulness element of contempt liability, the relator bears the burden of proving his inability to comply.”). Topletz has simply not carried his burden of proving the affirmative defense. Because the inquiry into whether civil contempt is justified is ongoing, see Shillitani, 384 U.S. at 371–72, Topletz could likely file a motion to lift the contempt and introduce evidence establishing that it is not possible for him to comply with the state court’s production order if he truly cannot get the documents, thereby succeeding on his affirmative defense. It is therefore unnecessary for the contempt order to explicitly permit Topletz to purge the contempt by other avenues in order to comply with due process, for the contempt judgment itself would be rescinded if Topletz demonstrated his inability to produce the documents. Put another way, either the contempt order contains a safety valve, or Texas’s substantive law of contempt provides one. The same result adheres regardless of whether the order contains a safety valve. In sum, Topletz has not established that using civil contempt to compel the production of items held by a third party is clearly contrary to established federal law. Topletz has thus not demonstrated a likelihood that the state court’s determination that the contempt order did not on its face violate the federal Due Process Clause was contrary to or an unreasonable application of clearly established federal law,[15] and he is accordingly unlikely to succeed on the merits of his first claim. Topletz Has Not Demonstrated that the State Court Clearly Erred in Finding Facts that Satisfied the Elements of Contempt. Topletz next contends that, even if it does not per se violate due process to use civil contempt to compel an individual to produce documents held by a third party, there was insufficient evidence for the state trial court to find him in contempt for failing to produce these specific documents.[16] It is well established that federal due process prohibits convicting an individual of a crime where, based on the evidence before the trial court, no rational trier of fact could have found the individual guilty of the charged offense. See Jackson v. Virginia, 443 U.S. 307, 324 (1979). This rule is recognized in the AEDPA standard of habeas review, which permits a federal court to grant relief if a state court judgment “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d)(2). In Texas, there are three elements that must be proven in order for an individual to be found in contempt of court. A court must find that there exists: “(1) a reasonably specific order; (2) a violation of the order; and (3) the willful intent to violate the order.”[17] Chambers, 898 S.W.2d at 259. An inability to comply with the order is considered an affirmative defense that the potential contemnor bears the burden of proving. Id. at 261 (citing Ex parte Kollenborn, 276 S.W.2d 251, 253–54 (Tex. 1955)). As a threshold issue, Topletz argues and the district court found that the state court was required to find that these elements were satisfied by clear and convincing evidence. Although the federal standard for civil contempt requires that contempt be demonstrated by clear and convincing evidence, see U.S. v. Rizzo, 539 F.2d 458, 465 (5th Cir. 1976), Topletz has cited no cases indicating that Texas employs this evidentiary standard in its courts or that the federal Due Process Clause mandates that the standard be used in state proceedings. But because the standard would be met in any event, we assume arguendo that it applies. Sufficient evidence was introduced in the state court proceedings for the state trial court to find that each of the elements of contempt was satisfied. As to the first element—a reasonably specific court order—the state court’s June 27, 2018 production order included several directives to Topletz. In addition to the interlined statement under the judge’s signature stating that “Defendant shall produce the trust documents and the tax returns as requested,” the order incorporated several of Willis’s discovery requests, specifically commanding Topletz to produce “any documents related to [the trust and] responsive to Plaintiff’s Request Nos. 9, 10, 14, 18, 27, and 28.” Those requests were, in turn, for: All certificates evidencing ownership of common or preferred capital stock in any corporation, mutual fund, bond fund or investment trust issued to you or any attorneys-in-fact, agents, servants, employees or trustees acting on your behalf or for your interest during the last five (5) years. All leases or other executory contracts of whatever kind or nature to which you are a party or in which you have any legal or equitable interest and/or have had any legal or equitable interest during the last five (5) years. . . . . 14. All financial statements, including balance sheets and profit and loss statements issued from January, 2012, to the present, by any business in which you have owned any legal equitable interest. . . . . 18. A complete list of all accounts and notes receivable due to any of Your parent companies, subsidiaries, and/or affiliates showing amounts owed and names of entitles owing funds to any business which you have any legal or equitable interest covering the period from January, 2013, to the present. . . . . For the last three (3) years, every Entity agreement (for example, articles of incorporation, certificates of formation, etc.) for every Entity that you have or had any interest in. All share certificates and other documents indicating ownership in any type of corporation, limited liability company or any type of partnership in which you have an interest and/or have had an interest in the last five (5) years. Topletz makes no argument that these requests, in conjunction with the state court’s specification that he produce everything responsive to them that was related to the trust, were not sufficiently clear or specific for him to know what was expected of him. Regarding the second contempt element, a violation of the order, the state court found that Topletz had failed to produce six different categories of documents related to the trust that he had been ordered to turn over. Topletz argues that two of the documents the court found he failed to produce were not included in the state trial court’s June 27, 2018 production order. Specifically, he contends that Willis had requested only balance sheets and profit and loss statements related to Topletz’s businesses, and the court’s production order incorporating the requests therefore did not extend to the trust’s balance sheet and profit and loss statements. Similarly, Topletz contends that the trust’s tax returns, which the court faulted him for not producing, were not covered by any of the identified discovery requests or the court’s order to produce “the tax returns as requested.” Yet, even if Topletz is correct, he raises no argument that any of the other four categories of documents that the court found he failed to produce were not clearly covered by the state court’s production order, nor that the state court clearly erred in finding that he had failed to turn these four categories of documents over. Topletz’s failure to produce any of the documents that he was ordered to turn over would constitute a violation of the court’s production order, and Topletz essentially concedes that he failed to produce several categories of documents that were included in the order. Thus, sufficient evidence existed for the state court to find that the second element of contempt—a violation of the court order—was also satisfied. As to the final element of contempt, the district court appears to have found that, given Topletz’s awareness of the order and lack of effort to comply with its terms, Topletz’s failure to comply was willful. Indeed, the court described his failure as a “refusal to comply.” Topletz’s only argument to the contrary is that there was no evidence that he was able to produce the documents. But this contention fails to recognize that, under Texas law, it is his burden to prove an inability to comply with the court’s order. See Chambers, 898 S.W.2d at 261 (“Although the inability to comply defense technically rebuts the willfulness element of contempt liability, the relator bears the burden of proving his inability to comply.”). Thus, the operative question is not whether there was any evidence showing his ability to produce the documents, but rather whether he introduced evidence showing his inability. Topletz offers only the letter from the trustee purporting to deny his request for the documents, but the state court was within its rights to find this evidence was outweighed by the evidence of the terms of the trust agreement, which gave Topletz a legal right to obtain the documents. Under AEDPA, it is Topletz’s burden to rebut the presumption that the district court’s factual conclusions were correct by clear and convincing evidence. 28 U.S.C. § 2254(e)(1). He has not demonstrated that the district court’s conclusions that the elements of contempt were satisfied were “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” Id. § 2254(d)(2). Accordingly, he has not shown a substantial likelihood of success on his second claim. Conclusion Based on the foregoing, Topletz has failed to show that the district court erred in finding that he is not likely to succeed on the merits of his habeas petition, which is a necessary condition for the issuance of a preliminary injunction. We therefore AFFIRM the district court’s denial of his motion for a preliminary injunction.