Duane “Butch” O’Malley is serving ten years in prison for violating the Clean Air Act by improperly removing and disposing of insulation containing regulated asbestos. See 42 U.S.C. § 7413(c)(1); 40 C.F.R. §§ 61.145, 61.149, 61.150, 61.154. After we upheld his convictions on direct appeal, United States v. O’Malley, 789 F.3d 1001 (7th Cir. 2014), O’Malley filed in the district court what he dubbed a motion under Federal Rule of Criminal Procedure 33(b)(1) for a new trial based on newly discovered evidence. That rule authorizes a district court to grant a timely request for a new trial “if the interest of justice so requires.” Fed. R. Crim. P. 33(a). The district court concluded that O’Malley’s submission contains constitutional theories that, the court reasoned, are incompatible with Rule 33 and cognizable only under 28 U.S.C. § 2255. And the remainder of O’Malley’s motion could not entitle him to relief under Rule 33, the court added, because the new evidence is not material. We conclude that the entirety of O’Malley’s submission falls within the scope of Rule 33(b)(1) even if his theories overlap with §2255, and that the district court should have respected his choice between these available means of relief. We thus vacate the district court’s decision and remand for further proceedings.
I. Background
The facts of this case and the challenges O’Malley raised on direct appeal are described fully in our earlier opinion, O’Mal-ley, 739 F.3d at 1003-06, but we provide a brief summary as necessary to understand the current appeal. Michael Pinski hired O’Malley’s company to replace the sprinkler system in a building that Pinski knew to have asbestos. O’Malley offered to remove the insulation for an additional cost and, after Pinski’s warning that some of it contained asbestos, assured Pinski that he would remove and dispose of the insulation properly. One of O’Malley’s employees, James Mikrut, cautioned O’Malley that the building was “probably all asbestos” and another said that O’Malley needed a license to remove asbestos. O’Malley eventually hired four people for the job, and they wore light protective equipment while using a circular saw to strip dry insulation off the pipes, producing large amounts of asbestos dust. An asbestos-abatement company refused to accept the discarded ■ asbestos insulation, so Mikrut and two other employees dumped garbage bags full of insulation in an abandoned farmhouse, a store dumpster, and a field near a vacant house. Inspections by the Environmental Protection Agency and its Illinois counterpart eventually led to O’Malley’s confession that he had not halted the work even after suspecting the material to be asbestos. Testing confirmed the material to be a regulated type of asbestos at high concentrations. O’Malley, Pinski, and Mikrut were indicted in June 2010. Pinski and Mikrut pleaded guilty and testified against O’Malley at his jury trial in September 2011. On direct appeal O’Malley principally argued that, because not all asbestos is regulated, the government had failed to prove that he knew' the building contained regulated asbestos. We rejected that argument, concluding that asbestos is so dangerous and the probability of regulation is so great that anyone working with the material would be presumed to know the applicable regulations. Id. at 1007 (citing United States v. Int'l Minerals & Chem. Corp., 402 U.S. 558, 565, 91 S.Ct. 1697, 29 L.Ed.2d 178 (1971)).
*812Two months after our decision, O’Malley (proceeding pro se) filed what he labeled as a motion under Rule 33 seeking a new trial based on newly discovered evidence.1 O’Malley asserted that, through a posttrial demand under the Freedom of Information Act and other “investigative work,” he had obtained new evidence that discredited Pinski, who was critical to establishing O’Malley’s knowledge of the asbestos. O’Malley separated the new evidence into three groups: (1) information withheld from him at the time of trial about Pinski’s ongoing cooperation with federal authorities investigating Pinski’s involvement in organized crime; (2) correspondence and agreements between Pinski and the Illinois EPA, which, O’Malley says, demonstrate that Pinski steered him to violate the Clean Air Act unintentionally; and (3) an appraisal of Pinski’s property done after the asbestos removal that, O’Malley asserts, contradicts Pinski’s trial testimony.
The district court first addressed O’Mal-ley’s motion in May 2014. The court, following O’Malley’s lead, separated the evidence into the same three groups and then denied “claim three” (the property appraisal) under Rule 33. The court reasoned that the appraisal, even if previously unavailable ' to O’Malley, would have been “merely impeaching or cumulative” and unlikely to lead to acquittal. As for the other two “claims,” however, the district court concluded that O’Malley could proceed only under § 2255. The court determined that Rule 83 motions based on newly discovered evidence are limited to situations in which (1) the new evidence establishes actual innocence and (2) the manner in, which the new evidence came to light after trial does not suggest a constitutional violation. Although it was only for the first category of evidence' that O’Malley had invoked Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), the district court concluded that Brady and Giglio applied to the second category as well and that O’Malley was relegated to raising both in a motion to vacate his sentence under § 2255 rather than a motion under Rule 33. The court gave O’Malley a deadline either to withdraw the motion or, if he preferred, amend it to include any other available § 2255 claims. See Castro v. United States, 540 U.S. 375, 383, 124 S.Ct. 786, 157 L.Ed.2d 778 (2003).
O’Malley moved for reconsideration, insisting that his submission, in its entirety, is a bona fide Rule 33 motion. He also asserted that he is innocent and that the new evidence establishes that he did not “knowingly” deal with regulated asbestos. He pressed for a new trial or at least an evidentiary hearing, under Rule 33, on all three of his assertions of newly discovered evidence. In the alternative, O’Malley requested more time to amend his submission if the district court was inflexible about construing part of it as a § 2255 motion. In June 2014 the district court entered a “text order” denying all relief and noting that the first and second “claims” would be deemed withdrawn *813“without prejudice to bringing them, and any other applicable collateral claims, ;as a properly filed [§ ] 2255 motion within the applicable limitations period.”2
II. ANALYSIS
O’Malley argues that the district court erred in concluding that his post-judgment motion is not a legitimate Rule 33 motion, and instead must be a § 2255 motion, to the extent that it relies on Brady and Giglio3 Although Rule 33 decisions typically are reviewed for abuse of discretion, see United States v. Berg, 714 F.3d 490, 500-01 (7th Cir. 2013); United States v. Palivos, 486 F.3d 250, 255 (7th Cir. 2007), we review de novo the legal issue whether a claim is cognizable in a Rule 33 motion, see United States v. Lawson, 810 F.3d 1032, 1042 (7th Cir. 2016); United States v. Knope, 655 F.3d 647, 660 (7th Cir. 2011).
We conclude that a postjudgment motion based on newly discovered evidence which happens to invoke a constitutional theory can be brought under Rule 33(b)(1) or § 2255, and thus O’Malley should have been allowed to choose the procedural vehicle. First, nothing in the text of Rule 33 excludes claims of newly discovered evidence that rely on a constitutional theory, such as the rule of Brady and Giglio. Rather a district court may “grant a new trial if the interest of justice so requires.” Fed. R. Crim. P. 33(a); see United States v. Peterson, 823 F.3d 1113, 1122 (7th Cir. 2016). A time constraint is the- only textual limit in the rule, and O’Malley’s motion resting on newly discovered evidence was timely filed within three years of his trial. See Fed. R. Crim. P. 33(b)(1). We have explained that, under Rule 33(b)(1), the “interest of justice” requires a new trial if additional evidence (1) was discovered after trial, (2) coiild not have been discovered sooner through the exercise of due diligence, (3) is material and not merely impeaching or cumulative, and (4) probably would have led to acquittal. See United States v. Westmoreland, 712 F.3d 1066, 1072 (7th Cir. 2013); United States v. Hagler, 700 F.3d 1091, 1101 (7th Cir. 2012); United States v. Reyes, 542 F.3d 588, 595 (7th Cir. 2008). And, like our sister circuits, we routinely evaluate Brady, Giglio, and other constitutional claims that were raised in postjudgment Rule 33(b)(1) motions. See, e.g., United States v. Salem, 578 F.3d 682, 685-90 (7th Cir. 2009) (Brady claim); United States v. L.E. Myers Co., 562 F,3d 845, 852, 856 (7th Cir. 2009) (Brady claim); United States v. Ervin, 540 F.3d 623, 630-32 (7th Cir. 2008) (Brady claim); United States v. Calderon, No. 15-1652, 829 F.3d 84, 89-90, 2016 WL 3854228, at *4 (1st Cir. July 15, 2016) (Brady and Giglio claim); United States v. Rafidi, No. 15-4095, 829 F.3d 437, 446-47, 2016 WL 3670273, at *6 (6th Cir. July 11, 2016) (Brady claim); United States v. Schneider, 801 F.3d 186, 201-02 (3d Cir. 2015) (Brady claim); United States v. Bow*814en, 799 F.3d 336, 351-52 (5th Cir. 2015) (claim of prosecutorial misconduct); United States v. Parse, 789 F.3d 83, 108-110 (2d Cir. 2015) (claim of juror bias); United States v. Flores-Rivera, 787 F.3d 1, 15-16 (1st Cir. 2015) (Brady claim); United States v. Isaacson, 752 F.3d 1291, 1309 (11th Cir. 2014) (Brady claim); United States v. Hoyle, 751 F.3d 1167, 1171 (10th Cir. 2014) (Brady claim); United States v. Battles, 745 F.3d 436, 446-47 (10th Cir. 2014) (Brady claim); United States v. Sessa, 711 F.3d 316, 321 (2d Cir. 2013) (Brady claim); United States v. Moore, 709 F.3d 287, 292-93 (4th Cir. 2013) (Brady claim); United States v. Rubashkin, 655 F.3d 849, 857-58 (8th Cir. 2011) (claim of judicial bias); United States v. Robinson, 627 F.3d 941, 948-52 (4th Cir. 2010) {Brady claim and claim of police misconduct).
Here the district court held that O’Mal-ley “is seeking relief that he can only obtain through § 2255,” relying on our decisions in United States v. Evans, 224 F.3d 670 (7th Cir. 2000), Ruth v. United States, 266 F.3d 658 (7th Cir. 2001), and United States v. Rollins, 607 F.3d 500 (7th Cir. 2010), for the proposition that Rule 33 does not authorize a postjudgment motion based on newly discovered evidence except when that evidence implies the defendant’s actual innocence and came to light after trial in a manner not suggesting a constitutional violation. That reliance is mistaken. Those decisions, which analyze some of the interplay between Rule 33 and § 2255, do not purport to define the outer limits of claims that can be brought under Rule 33.
First, in Evans we concluded that a legitimate, postjudgment claim of actual innocence based on newly discovered evidence would fall within the scope of Rule 33 but not § 2255. 224 F.3d at 672-74. We reasoned that motions to vacate under § 2255 are limited to claims that the defendant’s conviction or sentence was obtained in violation of the Constitution or a statute, and thus relief under § 2255 may not be available absent a constitutional or statutory error even if new evidence shows a factual injustice. See id. at 673-74; see also McQuiggin v. Perkins, — U.S.-, 133 S.Ct. 1924, 1931-32, 185 L.Ed.2d 1019 (2013) (explaining that, although the Supreme Court has not yet recognized right to habeas relief based on standalone innocence claim, actual innocence may excuse procedural default of underlying claim); but see United States v. Berry, 624 F.3d 1031, 1040 n.5 (9th Cir. 2010) (noting that Ninth Circuit recognizes freestanding innocence claim under § 2255). In Evans, though, we did not hold that an assertion of actual innocence is essential to a Rule 33 motion. A theory that newly discovered evidence establishes the defendant’s innocence is one, not the only, theory that would support relief under Rule 33, as the rule encompasses all claims based on newly discovered evidence which likely would lead to acquittal whether or not because of actual innocence. See United States v. Woods, 169 F.3d 1077, 1078 (7th Cir. 1999) (recognizing that Rule 33 would also be ground for retrial if newly discovered evidence “would lead to the suppression of critical evidence, and thus to the acquittal of a person who actually committed the crime”); United States v. Jordan, 806 F.3d 1244, 1252 (10th Cir. 2015) (newly discovered evidence under Rule 33 must be “of such a nature that in a new trial it would probably produce an acquittal” ’(quoting United States v. McCullough, 457 F.3d 1150, 1167 (10th Cir. 2006))); Bowen, 799 F.3d at 349 (newly discovered evidence under Rule 33 “may be relevant to any controlling issue of law” and “need not relate only to guilt or innocence”); Weaver v. United States, 793 F.3d 857, 863 (8th Cir. 2015) (“When newly discovered evidence is the ground for a §2255 motion, the district court should apply the same substantive test which governs a motion *815for a new trial under Fed. R. Crim. P. 33 premised upon the same ground.” (quotation marks and citation omitted)); United States v. Forbes, 790 F.3d 403, 406-07 (2d Cir. 2015) (newly discovered evidence under Rule 33 must be likely to result in acquittal); United States v. McGee, 763 F.3d 304, 321 (3d Cir. 2015) (new evidence must “probably produce an acquittal” (citation omitted)); United States v. Scrushy, 721 F.3d 1288, 1304-05 (11th Cir. 2013) (newly discovered evidence “must be such that it would probably produce án acquittal” but “need not relate directly to the issue of guilt or innocence”).
Nor did we hold in Evans that a theory of constitutional or statutory error established through newly discovered evidence could never be brought under Rule 33. To the extent that some language in our- decisions in Ruth and Rollins may imply such a holding in Evans, we disavow that interpretation. In Ruth, the defendant contended that he had received new evidence (through a request under the Freedom of Information Act) which bolstered his claim of innocence, and we concluded this theory was properly brought under Rule 33. See 266 F.3d at 660-61. But, relying on Evans, we added in dicta that if the defendant had included a Brady claim it would have fallen only under § 2255, see id. at 661, although Evans does not command that conclusion. Then, in Rollins, the bulk of our decision considers the jurisdictional implications of a motion to reconsider the denial of a motion for a new trial based on newly discovered evidence. See 607 F.3d at 501-04. After acknowledging that the district court had determined that the evidence relied on by the defendant was not newly discovered, we stated that he should have brought his action under § 2255 instead of Rule 33 because he had asserted constitutional errors. See id. at 504. But, consistent with other circuits, we have assessed constitutional theories in the context of post-judgment Rule 33(b)(1) motions based on newly discovered evidence since Evans was decided. We now clarify that; a motion for a new trial based on newly discovered evidence that demonstrates constitutional or statutory error may indeed be brought under Rule 33 and should be granted “if the interest of justice so requires.” Fed. R. CRIM. P. 33(a).
Here, O’Malley asserted that- he possesses newly discovered evidence which, he insists, would lead to his acquittal. Some of that evidence, he says, was withheld by the government in violation of the rule of Brady and Giglio, which presents a constitutional claim cognizable under § 2255. But when overlapping remedies are available, a prisoner is permitted to choose which to invoke. See United States v. Boyd, 591 F.3d 953, 956-57 (7th Cir. 2010) (expressly contrasting Evans and allowing defendant’s Rule 35(a) motion to proceed even though claim also could have been brought under § 2255); Collins v. Holinka, 510 F.3d 666, 667 (7th Cir. 2007) (“Persons who initiate independent litigation are entitled to have it resolved under the grant of authority they choose to invoke.”). And here O’Malley chose to use Rule 33. There was no need to recast his submission as one under § 2255 because there was no need to prevent him from “circumventing” the requirement of the Antiterrorism and Effective Death Penalty Act of 1996 that our permission be- obtained before filing a second or successive § 2255 motion. See 28 U.S.C. § 2244(b)(3); Poe v. United States, 468 F.3d 473, 476 (7th Cir. 2006). The Supreme Court has said only that a district court must warn a prisoner and provide an opportunity to withdraw or amend the motion if the court chooses to recharacterize that filing as a § 2255 motion. See Castro, 540 U.S. at 383, 124 S.Ct. 786; see also Figuereo-Sanchez v. United States, 678 F.3d 1203, 1206-07 (11th Cir. 2012); United States v. Black-*816stock, 513 F.3.d 128, 134 (4th Cir. 2008); In re Wagner, 421 F.3d 275, 278 (3d Cir. 2005). In Castro, the Court did not require that district courts recharacterize a motion as one under § 2255. See Henderson v. United States, 264 F.3d 709, 711 (7th Cir. 2001) (“Nothing in AEDPA says that a motion not labeled as a section 2255 motion shall nevertheless be deemed one if it could have been so labeled accurately. This is a purely judge-made rule, and so its contours are up to the judges to draw.”); Zelaya v. Sec’y, Fla. Dep’t of Corr., 798 F.3d 1360, 1366-67 (11th Cir. 2015) (allowing a prisoner to proceed, albeit unsuccessfully, under § 2241 instead of § 2255 since he emphatically had insisted that was his choice). One reason that district courts should warn about the consequences of recasting a submission is to help the prisoner decide “whether he should contest the recharacterization.” Castro, 540 U.S. at 384, 124 S.Ct. 786. The sequence of events in O’Malley’s case allowed him the option of filing a timely Rule 33 motion or a timely § 2255 motion, and he several times said that he wanted to use Rule 33 instead of § 2255.
III. Conclusion
Because the district court improperly required O’Malley to bring pieces of his evidence in a separate action, we vacate the ruling and direct the district court to allow him to proceed under Rule 33. We express no opinion on the underlying merits of O’Malley’s motion.
. This submission was O'Malley’s third denominated as a Rule 33 motion. His first, filed the day after his trial ended and denied two months later, claimed legal errors not relevant here. The second, hied while O’Malley's direct appeal was pending, also rested on what he described as newly discovered evidence — some of it included in his present submission — but was withdrawn after the district court warned O'Malley that his motion would be construed as one under 28 U.S.C. §2255. Rule 33 does not limit the number of motions for new trial grounded on newly discovered evidence, so long as the motions are filed within three years of the verdict. Fed. R. Crim. P. 33(b)(1). O’Malley's trial was in September 2011, and he filed his current submission within three years, in March 2014.
. After the Supreme Court of the United States denied certiorari from our decision upholding O’Malley’s convictions,-U.S.-, 135 S.Ct. 411, 190 L.Ed.2d 298 (Oct. 20, 2014), he separately filed a timely § 2255 motion claiming actual innocence, No. 15-cv-2213 (C.D. Ill. Sept. 24, 2015).
. O'Malley appealed in August 2014, seeking to challenge both the initial, written decision from May 2014 and the text order from June 2014. The district court granted him an extension of time to appeal, purporting to limit that extension to the June text order denying the motion to reconsider. But the district court did not fully dispose of O’Malley’s motion for a new trial until entering the text order, and O’Malley filed his notice of appeal within the deadline (as extended by the district court) measured from that order. Thus his notice of appeal is sufficient for us to review the district court's May 2014 written decision as well.