Defendant-appellant Jose Peña was charged in the United States District Court for the Southern District of New York in five counts of an eight-count indictment in connection with the killings of Jose Suarez and Juan Carmona. Counts Four, Five, and Six charged Peña with conspiring to commit, and committing, murder for hire in violation of 18 U.S.C. §1958. Counts Seven and Eight charged Peña with use of a firearm to commit murder in violation of 18 U.S.C. §924(j). Peña was convicted on all five counts and received a sentence of five concurrent life terms, one for each count. In response to intervening Supreme Court precedent, Peña filed a motion pursuant to 28 U.S.C. §2255 asserting that his two §924(j) convictions on Counts Seven and Eight should be vacated. The district court (Marrero, Judge) agreed, and granted the motion. The court declined, however, to resentence Peña de novo. Peña argues that this was error, either because de novo resentencing was mandatory, or because the district court abused its discretion in declining to resentence Peña de novo. We conclude that §2255′s statutory text vests district courts with the discretion to decide when to conduct a de novo resentencing and that de novo resentencing was not mandatory here. We also conclude that because resentencing Peña would have been “strictly ministerial,” resulting in the same sentence of mandatory life imprisonment that he received in the first instance, the district court did not abuse its discretion. We therefore AFFIRM the district court’s July 6, 2020 amended judgment and its December 17, 2020 order. ROBERT SACK, C.J. Defendant-appellant Jose Peña was charged in the United States District Court for the Southern District of New York in five counts of an eight-count indictment in connection with the killings of Jose Suarez and Juan Carmona. Counts Four, Five, and Six charged Peña with conspiring to commit, and committing, murder for hire punishable by life imprisonment under 18 U.S.C. §1958. Counts Seven and Eight charged Peña with use of a firearm to commit murder punishable by life imprisonment under 18 U.S.C. §924(j). Peña was convicted on all five counts. The district court sentenced him to five concurrent terms of life imprisonment. In response to intervening Supreme Court precedent, Peña filed a motion pursuant to 28 U.S.C. §2255 asserting that his two §924(j) convictions on Counts Seven and Eight should be vacated. The district court (Marrero, Judge) granted the motion, but it did not resentence Peña de novo. Peña argues that this was error, either because de novo resentencing was mandatory, or because the district court abused its discretion in declining to resentence Peña de novo. We conclude that §2255′s statutory text vests district courts with discretion in such circumstances to decide whether or not to conduct a de novo resentencing; de novo resentencing was not, under the circumstances presented here, mandatory. We also conclude that because resentencing Peña would have resulted in the same sentence of mandatory life imprisonment as to which he was originally sentenced, the district court did not abuse its discretion in declining to engage in such a strictly ministerial de novo resentencing. BACKGROUND A. Factual Background On April 15, 2013, a Southern District grand jury returned an eight-count indictment against Jose Peña and two others, including Peña’s brother. Peña was charged in five of the eight counts. Count Four charged him with conspiracy to commit murder for hire in violation of 18 U.S.C. §1958, alleging that he conspired to kill Jose Suarez, which resulted in the deaths of Suarez and Juan Carmona. Count Five charged Peña with murder for hire in violation of 18 U.S.C. §§2 and 1958 for the killing of Suarez. Count Six charged him with murder for hire in violation of 18 U.S.C. §§2 and 1958 for the killing of Carmona. Count Seven charged him with use of a firearm to commit murder for the killing of Suarez in violation of 18 U.S.C. §§2 and 924(j), both in relation to a crime of violence — the conspiracy to commit murder for hire charged in Count Four of the indictment — and in relation to an uncharged drug trafficking conspiracy. Count Eight charged Peña with use of a firearm to commit murder for the killing of Carmona in violation of 18 U.S.C. §§2 and 924(j), both in relation to a crime of violence — the conspiracy to commit murder for hire charged in Count Four of the indictment — and in relation to an uncharged drug trafficking conspiracy. Trial began on October 15, 2013. At trial, the government proffered evidence that Peña and his brother disguised themselves as police officers; used those disguises to stop and kidnap Suarez and Carmona on June 25, 1997; fatally shot them; and set fire to their bodies. The government’s case included, among other evidence, the testimony of more than two dozen witnesses; ballistics reports; crime-scene evidence including video surveillance and handcuffs used in the disguise; and a gun recovered from Peña’s brother, Hector. The district court’s instruction to the jury on Count Four included the statement: “[Y]ou may find the defendants guilty of the crime of conspiring to commit a murder for hire even if no murder for hire was actually committed. Conspiracy is a crime, even if the conspiracy was not successful. Substantive murder for hire is also charged in Counts Two, Five and Six, as you know.” Jose Peña App’x 44, Excerpts of Jury Trial dated October 28, 2013. That portion of the instruction was erroneous. While the jury was not required to find that a victim of the crime died in order to convict Peña for violating 18 U.S.C. §1958(a), such a finding was required to subject Peña to the enhanced punishment of death or life imprisonment. See 18 U.S.C. §1958(a) (providing inter alia that whoever conspires to use interstate commerce to commit murder for hire shall be imprisoned for not more than ten years if death or personal injury does not result and punished by death or life imprisonment if death does result); see also Burrage v. United States, 571 U.S. 204, 210 (2014) (concluding while interpreting an unrelated statute that “[b]ecause the ‘death results’ enhancement increased the minimum and maximum sentences to which [the defendant] was exposed, it is an element that must be submitted to the jury and found beyond a reasonable doubt”). Similarly, the district court erroneously instructed the jury regarding Counts Five and Six, stating that: “The government does not have to prove that the murder was committed or even that it was attempted. It must prove that the travel in interstate or foreign commerce or the use of the facility of interstate or foreign commerce was done with the intent to further or facilitate the commission of the murder.” Jose Peña App’x 44, Excerpts of Jury Trial dated October 28, 2013. Again, the instruction was erroneous inasmuch as the jury was indeed required to find that death resulted to subject Peña to the maximum punishment for these offenses. See 18 U.S.C. §1958(a). Trial concluded on October 29, 2013. The jury convicted Peña on all five counts against him. On December 19, 2014, the district court held Peña’s sentencing hearing. The Presentence Report (“PSR”) concluded that the three §1958 counts qualified for a mandatory life sentence, the two §924(j) counts carried a maximum sentence of life imprisonment, and the Sentencing Guidelines range was life. The district court sentenced Peña to five concurrent terms of life imprisonment, one for each count, and imposed a $500 mandatory special assessment. Procedural History Peña appealed to this Court, which affirmed the district court’s judgment in 2016. See United States v. Francisco, 642 F. App’x 40, 45-46 (2d Cir. 2016) (summary order). Later that same year, Peña moved pursuant to §2255 to vacate his convictions on several grounds including ineffective assistance of counsel. See Pena v. United States, 192 F. Supp. 3d 483, 486-87 (S.D.N.Y. 2016). The district court denied the motion. Id. at 496. In 2017, Peña moved in this Court for a certificate of appealability. See Pena v. United States, 334 F. Supp. 3d 578, 579 (S.D.N.Y. 2018) (explaining procedural history). We dismissed the appeal because the notice of appeal was untimely. See id. Later in 2017, Peña again moved to reopen his §2255 proceeding. Id. In 2018, the district court denied that motion. Id. at 578. Peña then moved in this Court for a certificate of appealability, which we denied in 2019. See Pena v. United States, No. 18-3315, 2019 WL 11891995, at *1 (2d Cir. Apr. 10, 2019). In February 2020, Peña moved in this Court for permission to file another §2255 motion in light of United States v. Davis, 139 S. Ct. 2319 (2019). Davis held that an offense could qualify as a predicate “crime of violence” for purposes of §924(c) only if it was a felony that “ha[d] as an element the use, attempted use, or threatened use of physical force against the person or property of another.” Id. at 2323-24 (citation omitted); see also id. at 2336 (declaring unconstitutional a separate clause of §924(c) that defined a predicate “crime of violence” as a felony “that by its nature, involves a substantial risk that physical force against the person or property of another may be used in the course of committing the offense” (citation omitted)). Peña argued that conspiracy to commit murder for hire no longer qualified as a “crime of violence” under 18 U.S.C. §924(j) because such a conspiracy does not require actual or threatened use of physical force. We granted Peña permission to file another §2255 motion. See Pena v. United States, No. 19-1545, 2020 WL 6846397, at *1 (2d Cir. July 15, 2020). The government consented to the vacatur of Peña’s convictions on Counts Seven and Eight, agreeing that those convictions could not stand after Davis. On July 6, 2020, the district court granted Peña’s motion to vacate Counts Seven and Eight. However, the court decided that a full resentencing was not warranted “[b]ecause vacatur of Counts Seven and Eight will not affect Peña’s other convictions, each of which carries a mandatory term of life imprisonment.” Jose Peña App’x 68, Order dated July 6, 2020. The district court amended the judgment to reflect concurrent sentences of life imprisonment on Counts Four, Five, and Six. Peña moved for reconsideration. He argued that de novo resentencing was mandatory, citing United States v. Rigas, 583 F.3d 108, 115-16 (2d Cir. 2009). He also argued that, because the court erroneously failed to instruct the jury to determine whether death resulted from the murder-for-hire conspiracy described in the three §1958 counts, the district court erred in denying de novo resentencing. Peña claimed that, because the jury did not specifically find that death was a result of Peña’s offenses in Counts Four, Five, and Six, the district court could sentence him to only ten years of imprisonment on each of those counts. On December 17, 2020, the district court denied Peña’s motion for reconsideration. It reasoned that the “rule requiring de novo resentencing” is “expressly limited to instances in which a conviction was overturned on direct appeal” and “does not apply in the Section 2255 context.” Jose Peña App’x 94, Decision and Order dated December 17, 2020. The court also rejected Peña’s argument that — because of the deficient jury instructions for Counts Four, Five, and Six — Peña could be sentenced to no more than ten years on each count, stating that “in convicting Peña of Counts Seven and Eight, the jury necessarily found that Peña was a substantial factor in causing the victim’s death and also that the victim was in fact murdered, i.e., that death resulted.” Id. at 96 (internal quotation marks omitted). Peña timely appealed. DISCUSSION I. De Novo Resentencing Was Not Mandatory Section 2255 grants district courts the discretion to choose among four remedies when reviewing a sentence that was not authorized by law or is otherwise open to collateral attack. See 28 U.S.C. §2255(b). A court may: “[1] vacate and set the judgment aside and…discharge the prisoner or [2] resentence him or [3] grant a new trial or [4] correct the sentence as may appear appropriate.” Id. Peña relies on our decisions in United States v. Quintieri, 306 F.3d 1217 (2d Cir. 2002), and Rigas to argue that the district court was required to conduct a de novo resentencing. In Quintieri, we noted that “resentencing usually should be de novo when a Court of Appeals reverses one or more convictions and remands for resentencing.” 306 F.3d at 1228 (emphasis in original). In Rigas, we observed that Quintieri “created a ‘default rule’ that de novo resentencing is required where a conviction is reversed in part on appeal,” 583 F.3d at 115 (citation omitted), and underscored that this rule is “not a guideline,” id. at 117. But both Quintieri and Rigas were decided in the context of direct appeals, not collateral challenges pursuant to §2255. See Quintieri, 306 F.3d at 1227-28 (“When the conviction on one or more charges is overturned on appeal and the case is remanded for resentencing, the constellation of offenses of conviction has been changed and the factual mosaic related to those offenses that the district court must consult to determine the appropriate sentence is likely altered.” (emphasis added)); see also Rigas, 583 F.3d at 117 (“[R]esentencing is required where part of a conviction is reversed on appeal.” (emphasis added)). Peña argues that this is a distinction without a difference and urges us to extend the default rule in Rigas to the §2255 context. We decline to do so. Section 2255′s plain text, which vests district courts with discretion to select the appropriate relief from a menu of options, precludes us from applying the default rule in Rigas to all cases that arise in the §2255 context. District courts in this Circuit have come to a similar conclusion. For example, in United States v. Medunjanin, No. 10-cr-0019 (BMC), 2020 WL 5912323 (E.D.N.Y. Oct. 6, 2020), the district court held that “the default rule does not require a de novo resentencing in the §2255 context” because the “plain text of §2255 vests the Court ‘with the discretion to determine first the nature of the relief that ‘may appear appropriate,”” id. at *8 (citation omitted). Similarly, in Ayyad v. United States, No. 16-cv-4346 (LAK), 2020 WL 5018163 (S.D.N.Y. Aug. 24, 2020), the district court noted that it was not “aware of[] any case in which the Quintieri default rule has been applied in the habeas context” and reasoned that such a rule “would be in tension with the narrow scope of Section 2255,” id. at *2. We have held that judges have discretion with respect to resentencing in the §2255 context. In United States v. Gordils, 117 F.3d 99 (2d Cir. 1997), we rejected the defendant’s argument that district courts have no discretion to engage in de novo resentencing under §2255, id. at 104. “[A]t least in the context of a ‘truly interdependent sentence’ such as where a mandatory consecutive sentence affects the applicable offense level under the guidelines — the language of §2255 provides sufficient statutory authority for a district court to exercise its jurisdiction to resentence defendants ‘as may appear appropriate.’” Id. (citations omitted). Peña argues that the discretion discussed in Gordils was erased by Quintieri and Rigas. We conclude to the contrary that §2255′s statutory text continues to grant district courts discretion in the matter. The government argues that every circuit to analyze this issue has held that de novo resentencing is not required in this context. That appears to be correct. A recent opinion of the Sixth Circuit is instructive. In United States v. Augustin, 16 F.4th 227 (6th Cir. 2021), cert. denied, 142 S. Ct. 1458 (mem.) (2022), a defendant was convicted on eight counts of an indictment, including a conviction under §924(c) for using a firearm during a crime of violence, id. at 231. After Augustin argued that his §924(c) conviction was no longer valid under Davis, the district court vacated his §924(c) conviction and the corresponding 120-month sentence without a de novo resentencing. Id. Augustin argued on appeal that the district court should instead have resentenced him. Augustin, 16 F.4th at 231. The Sixth Circuit noted that resentencing is “akin to ‘beginning the sentencing process anew’” and requires a full sentencing hearing. Id. at 232 (citation omitted). A sentence correction, on the other hand, is appropriate when “it simply vacates ‘unlawful convictions (and accompanying sentences)’ without choosing to reevaluate ‘the appropriateness of the defendant’s original sentence.’” Id. (citation omitted). The Sixth Circuit concluded that “district courts have broad [but not unbounded1] discretion to choose between these remedies.” Id. At oral argument, Peña conceded that no other circuit has held that de novo resentencing is required in the §2255 context. See, e.g., Troiano v. United States, 918 F.3d 1082, 1087 (9th Cir. 2019) (“[T]he decision to unbundle a sentencing package — that is, to conduct a full resentencing on all remaining counts of conviction when one or more counts of a multi-count conviction are undone — rests within the sound discretion of the district court.”); United States v. Palmer, 854 F.3d 39, 49 (D.C. Cir. 2017) (“The district court was required to do no more, for Section 2255(b) accords it discretion in choosing from among four remedies, ‘as may appear appropriate.’”). We find our sister circuits’ reasoning to be persuasive. We conclude that §2255 grants district courts discretion in selecting a remedy. II. The District Court Did Not Abuse Its Discretion Peña argues that even if a district court is not required to conduct a de novo resentencing in the §2255 context after a conviction has been reversed, the district court abused its discretion by not resentencing Peña de novo. Peña bases his argument on the contention that — under the flawed jury instructions for Counts Four, Five, and Six — he was convicted of only the base offense under §1958: conspiring to commit, and committing, murder for hire. Inasmuch as that crime carries a ten-year maximum sentence, he asserts, a full resentencing would result in a significantly lower sentence on those counts. According to Peña, the district court did not fully appreciate these points and misunderstood the authority it had to impose a non-life sentence at his resentencing. Peña’s argument fails for two reasons. First, Peña’s argument regarding his §1958 convictions and the sentences he would receive on resentencing is procedurally defaulted. “In general, a defendant is barred from collaterally challenging a conviction under §2255 on a ground that he failed to raise on direct appeal.” United States v. Thorn, 659 F.3d 227, 231 (2d Cir. 2011). Peña had the opportunity to challenge the erroneous jury instructions associated with his convictions on Counts Four, Five, and Six before the verdict or after his trial. He did not do so. He then failed to raise the issue on his direct appeal. See Francisco, 642 F. App’x at 45 (describing Peña’s arguments on appeal). These failures constituted a procedural default.2 Peña asserts that “[t]he Government…attacks a straw person in arguing that such an argument is procedurally defaulted” because Peña is simply claiming that the district court abused its discretion when declining to resentence him. Appellant’s Reply Brief at 8-9. But Peña’s abuse-of-discretion argument is the same as the procedurally defaulted argument that the sentences he received on Counts Four, Five, and Six were unlawful because he was charged on erroneous jury instructions. See id. at 9 (“[T]he court mistakenly believed that resentencing was pointless because it would be required to reimpose the same life sentences on the §1958 counts at such a proceeding.”). A defendant can raise new arguments in a §2255 motion “if the defendant establishes (1) cause for the procedural default and ensuing prejudice or (2) actual innocence.” Thorn, 659 F.3d at 231. Peña cannot establish cause and prejudice or actual innocence; he does not even attempt to do so. We reject Peña’s attempt thus to sidestep the procedural-default rule. A district court’s decision to deny a defendant’s request for resentencing in the §2255 context does not empower a defendant to raise otherwise procedurally defaulted arguments against the merits of the defendant’s convictions and sentence.3 Second, even if Peña were allowed to raise his challenges to his sentences on Counts Four, Five, and Six in this §2255 motion, his challenges would fail. Peña contends that because the district court instructed the jury that it did not need to find that death resulted in order to convict him of these three counts, Peña’s sentences for those convictions may not exceed 10 years on each count, Counts Four, Five, and Six charged Peña with conspiracy to commit murder for hire, and murder for hire, in violation of §1958. This statute contains three levels of punishment depending on the result of the murder-for-hire conduct. Those who violate the base offense, use of interstate commerce in the commission of murder for hire, “shall be fined…or imprisoned for not more than ten years, or both.” 18 U.S.C. §1958(a). “[I]f personal injury results” from the base offense, violators “shall be fined…or imprisoned for not more than twenty years, or both.” Id. But “if death results, [violators] shall be punished by death or life imprisonment, or shall be fined not more than $250,000, or both.” Id. Peña is correct that the district court should have instructed the jury it needed to determine whether death was a result of the conduct alleged in Counts Four, Five, and Six. Under Alleyne v. United States, 570 U.S. 99 (2013), and Apprendi v. New Jersey, 530 U.S. 466 (2000), any fact, other than a prior conviction, that triggers statutory mandatory minimums and maximums must be found by a jury or admitted by the defendant. See Alleyne, 570 U.S. at 103 (“[A]ny fact that increases the mandatory minimum is an ‘element’ that must be submitted to the jury.”); Apprendi, 530 U.S. at 490 (“Other than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.”); see also United States v. Booker, 543 U.S. 220, 244 (2005) (holding that Apprendi is not violated when the relevant fact is “admitted by the defendant”). Whether death resulted is a fact that triggered a higher mandatory minimum sentence, and the district court erred by not instructing the jury to make a finding as to this fact if it determined that Peña was guilty of Counts Four, Five, and Six. But the district court’s error was harmless. Alleyne and Apprendi errors are subject to harmless-error analysis. See United States v. Confredo, 528 F.3d 143, 156 (2d Cir. 2008); United States v. Friedman, 300 F.3d 111, 127 (2d Cir. 2002). “In undertaking a harmless-error analysis, we must determine whether it appears beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained.” Friedman, 300 F.3d at 128 (internal quotation marks and citation omitted); see also Neder v. United States, 527 U.S. 1, 17 (1999) (“[W]here a reviewing court concludes beyond a reasonable doubt that the omitted element was uncontested and supported by overwhelming evidence, such that the jury verdict would have been the same absent the error, the erroneous instruction is properly found to be harmless.”). There is overwhelming evidence that the jury would have found that death was the result of the conduct alleged in Counts Four, Five, and Six had it received proper instructions. As an initial matter, Peña’s murder-for-hire conspiracy did result in the deaths of Suarez and Carmona, and the jury heard evidence of this fact at trial. The jury also convicted Peña of use of a firearm to commit murder in violation of 18 U.S.C. §924(j) in Counts Seven and Eight. The jury could not have returned this verdict without finding that Peña’s conduct resulted in death. Although Peña’s convictions on Counts Seven and Eight are no longer valid following Davis, the jury’s verdict demonstrates that it would have found that death resulted from Peña’s murder-for-hire conspiracy had it received proper instructions on Counts Four, Five, and Six. Peña objects to our inquiry into what the jury would have found had it received proper instructions, but he bases his objection largely on cases where the indictment failed to allege an element of the offense. See, e.g., United States v. Lang, 732 F.3d 1246, 1249 (11th Cir. 2013) (“We cannot combine the allegations from separate counts to allege what the indictment itself does not.”); see also United States v. Thomas, 274 F.3d 655, 667-69 (2d Cir. 2001) (en banc) (district court erred in sentencing defendant based on its own finding that the defendant’s crime involved a specific drug quantity when the indictment did not allege any specific drug quantity and the jury did not make a finding on this issue). There was no such indictment error here: Counts Four, Five, and Six of the indictment did allege that Peña’s murder-for-hire conspiracy resulted in death. And even if that allegation had been omitted, our case law makes clear that the mistaken omission of an element from an indictment is amenable to harmless-error analysis. See United States v. Confredo, 528 F.3d 143, 156 (2d Cir. 2008) (“[A]n Apprendi violation concerning an omission from an indictment is not noticeable as plain error where the evidence is overwhelming that the grand jury would have found the fact at issue. We think the same analysis should apply to harmless error.” (internal citation omitted)). Any such omission would have been harmless for the same reasons as the instructional error.4 Having concluded that Peña’s challenges to his §1958 sentences are defaulted and in any event meritless, we conclude the district court did not abuse its discretion in denying to resentence Peña de novo. Any resentencing would have been “strictly ministerial,” serving simply to delete the sentences on the now-vacated counts. Cf. United States v. Powers, 842 F.3d 177, 180 (2d Cir. 2016) (per curiam) (citation omitted). As noted in our discussion of Augustin above, a district court’s discretion to not conduct a de novo resentencing has limits. It may be that in most cases in which resentencing would not be strictly ministerial, a district court abuses its discretion when it denies de novo resentencing. But we need not and do not attempt today to define the circumstances under which a district court abuses its discretion in denying de novo resentencing. It is enough, in light of the facts of the case at bar, to conclude only that a district court may properly deny de novo resentencing when the exercise would be an empty formality, as it would be here. CONCLUSION We have considered Peña’s remaining arguments on appeal and conclude that they are without merit. For the reasons explained above, we AFFIRM the district court’s July 6, 2020 amended judgment and December 17, 2020 order.