Judge KEARSE concurs in the opinion and judgment of the Court, and files a concurring opinion.
JOSÉ A. CABRANES, Circuit Judge:
The principal question presented, as a matter of first impression, is whether the change in the law of this Circuit following United States v. Gaudin, 515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995), to require proof of materiality beyond a reasonable doubt for conviction under 18 U.S.C. § 1001, applies retroactively on eol-lateral review. Petitioner John C. Man-danici, Jr., appeals from a judgment of the United States District Court for the District of Connecticut (Alvin W. Thompson, Judge), entered December 4, 1998, denying his petition for a writ of error coram nobis.1 Judge Thompson held that. Gau-din does not apply retroactively insofar as the Supreme Court’s decision changed the law to require that materiality be decided by a jury rather than the judge, but he did not address Mandanici’s alternative argument concerning the standard of proof required for conviction after Gaudin. We hold that this latter change in law does not apply retroactively on collateral review, and therefore affirm the judgment of the District Court.
I.
The factual background of this case is described in detail in our opinion on direct appeal, see United States v. Mandanici, 729 F.2d 914 (2d Cir.1984), familiarity with which is assumed, and will be repeated here only to the extent necessary.
Mandanici owned an apartment building in Bridgeport, Connecticut, in the early 1980s, for which he sought and received rent subsidy benefits under a program funded by the United States Department of Housing and Urban Development (“HUD”). See id. at 915. To participate in the program, Mandanici was required, inter alia, to complete and file a number of documents with the Bridgeport Housing Authority, which administered the program locally on behalf of HUD. See id. at 915-16. In 1982, Mandanici was indicted by a federal grand jury sitting in the District of Connecticut on three counts of making false statements in these documents, in violation of 18 U.S.C. § 1001,2 and on a fourth count of making false statements to a federally insured bank, in [522]*522violation of 18 U.S.C. § 1014.3 See Mandanici 729 F.2d at 916 & n. 2.
In February and March 1983, Mandanici was tried before a jury, with Judge Robert C. Zampano presiding. When Mandanici was tried, § 1001 provided:
Whoever, in any matter within the jurisdiction of any department or agency of the United States knowingly and willfully falsifies, conceals or covers up by any trick, scheme, or device a material fact, or makes any false, fictitious or fraudulent statements or representations, or makes or uses any false writing or document knowing the same to contain any false, fictitious or fraudulent statement or entry, shall be fined not more than $10,000 or imprisoned not more than five years, or both.
18 U.S.C. § 1001 (1976).4 By its plain terms, the provision established three separate offenses: (1) falsifying, concealing, or covering up by any trick, scheme, or device a material fact; (2) making a false, fictitious, or fraudulent statement; and (3) making or using a false writing or document.5 A conviction under § 1001 could be sustained if the jury found that the requirements of any one of these three offenses had been met.
At the time of Mandanici’s trial, the law in this Circuit was that materiality was an element only of the first offense — namely, falsifying, concealing, or covering up by trick, scheme, or device a material fact. See, e.g., United States v. Marchisio, 344 F.2d 653, 666 (2d Cir.1965). Materiality in such cases, however, was not an issue to be decided by a jury, but rather an issue to be decided by the judge as a matter of law. See, e.g., United States v. Gribben, 984 F.2d 47, 50-51 (2d Cir.1993). A conviction for making false statements or for making or using false writings, on the other hand, did not require any finding of materiality. See United States v. Elkin, 731 F.2d 1005, 1009 (2d Cir.1984); see also United States v. Bilzerian, 926 F.2d 1285, 1299 (2d Cir.1991).
Although Mandanici was charged with making false statements, it appears that Judge Zampano believed materiality was an element of the offenses charged, albeit one to be decided by him rather than by the jury.6 Thus, at the close of Mandani-ci’s trial, Judge Zampano did not instruct [523]*523the jury that it had to find beyond a reasonable doubt that Mandanici’s statements were material; instead, Judge Zam-pano himself made a finding of materiality-7
Judge Zampano submitted the case to the jury on March 4, 1983. On the same day, the jury returned a verdict of guilty on all three counts of making false statements in violation of § 1001, and not guilty with respect to the charge under § 1014. On direct appeal, we reversed Mandanici’s conviction on one of the three § 1001 counts for insufficiency of the evidence, but affirmed his convictions on the other two, finding that the evidence “amply supported]” the charges. Mandanici, 729 F.2d at 920; see id. at 921. Mandanici served a three-year term of probation and paid a $20,000 fine.
In June 1995, the Supreme Court ruled that if materiality is an element under § 1001, a finding of materiality must be made by the jury, rather than by the judge. See United States v. Gaudin, 515 U.S. 506, 522-23, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995). The Supreme Court refrained from expressly deciding whether materiality is an element under § 1001,8 but in United States v. Ali, 68 F.3d 1468 (2d Cir.1995), amended on denial of reh’g, 86 F.3d 275 (2d Cir.1996), decided four months after Gaudin, we overruled our precedents and held that materiality is an element of any and all charges under § 1001. See id. at 1474-75. Accordingly, the law in this Circuit now requires that for a conviction under § 1001 to be sustained, the jury must have made a finding of materiality beyond a reasonable doubt.
On November 17, 1995, invoking Gaudin, Mandanici filed a petition for a writ of error coram nobis to vacate and expunge his convictions.9 Mandanici alleged that [524]*524his “[constitutional rights to due process and to a jury trial were violated by the trial court’s failure to instruct the jury that the government had the burden of proving beyond a reasonable doubt the element of materiality.” In an opinion filed December 4, 1998, Judge Thompson denied the petition, relying on our decision in Bilzerian v. United States, 127 F.3d 237 (2d Cir.1997), to hold that Gaudin does not apply retroactively on collateral review. This timely appeal followed.
II.
A writ of error coram nobis is “essentially a remedy of last resort for petitioners who are no longer in custody pursuant to a criminal conviction.” Fleming v. United States, 146 F.3d 88, 89-90 (2d Cir.1998) (per curiam). Coram nobis is “not a substitute for appeal, and relief under the writ is strictly limited to those cases in which errors of the most fundamental character have rendered the proceeding itself irregular and invalid.” Foont v. United States, 93 F.3d 76, 78 (2d Cir.1996) (internal quotation marks and ellipsis omitted); see Nicks v. United States, 955 F.2d 161, 167 (2d Cir.1992) (stating that a writ of error coram nobis should be granted “only where extraordinary circumstances are present”). In reviewing a petition for the writ, a court must presume that the proceedings were correct, and the burden of showing otherwise rests on the petitioner. See Nicks, 955 F.2d at 167.
To obtain coram nobis relief, a petitioner “must demonstrate that T) there are circumstances compelling such action to achieve justice, 2) sound reasons exist for failure to seek appropriate earlier relief, and 3) the petitioner continues to suffer legal consequences from his conviction that may be remedied by granting of the writ.’ ” Fleming, 146 F.3d at 90 (quoting Foont, 93 F.3d at 79). On appeal, we review de novo the question of whether a district judge applied the proper legal standard, but review the judge’s ultimate decision to deny the writ for abuse of discretion. See Fleming, 146 F.3d at 90.
A.
As noted, Judge Thompson denied Man-danici’s present petition on the ground that Gaudin does not apply retroactively on collateral review. In Gaudin, the Supreme Court held that if materiality is an element under § 1001, the Fifth and Sixth Amendments require that a jury, not a judge, make the finding. See 515 U.S. at 522-23, 115 S.Ct. 2310. Following Gaudin, we held in Ali that materiality is an element of any and all charges under § 1001. See 68 F.3d at 1474-75. Thus, while before Gaudin and Ali materiality in a prosecution under § 1001 could have been decided by the judge, or not at all (if materiality was not an element), now the issue is reserved for the jury in all cases.
In Bilzerian, we confronted the question of whether Gaudin and/or Ali applies retroactively on collateral review. Bilzerian had been convicted in 1989 of, inter alia, both concealing material facts and making false statements. See 127 F.3d at 239. In accordance with the law at the time (which was unchanged from 1983, when Mandanici was -tried), the trial judge made findings of materiality with respect to the charges of concealing material facts; in contrast, the judge neither made findings nor in[525]*525structed the jury concerning materiality with respect to the charges of making false statements. See id.10
In view of these facts, we engaged in a bifurcated analysis. First, with respect to Bilzerian’s conviction for concealing material facts, we held that Gaudin does not apply retroactively on collateral review. Applying the framework announced by the Supreme Court in Teague v. Lane, 489 U.S. 288, 301, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989) (plurality opinion), we decided as a threshold matter that the rule in Gaudin was a “new” rule of constitutional criminal procedure. See Bilzerian, 127 F.3d at 240-41. Under Teague, new rules of constitutional criminal procedure do not apply retroactively on collateral review unless they fall into either of two categories: (1) new rules that “place an entire category of primary conduct beyond the reach of the criminal law, or new rales that prohibit imposition of a certain type of punishment for a class of defendants because of their status or offense”; or (2) “new watershed rules of criminal procedure that are necessary to the fundamental fairness of the criminal proceeding.” Sawyer v. Smith, 497 U.S. 227, 241-42, 110 S.Ct. 2822, 111 L.Ed.2d 193 (1990) (internal quotation marks and citation omitted). We resolved that the Gaudin rale does not fall into either of these categories, and therefore held that it does not apply retroactively on collateral review. See Bilzerian, 127 F.3d at 241. The rule in Gaudin, we reasoned, “merely shifts the determination of materiality from the judge to the jury ... [and tjhere is little reason to believe that juries will have substantially different interpretations of materiality than judges.” Id.
In contrast, we concluded that the holding of Ali, that materiality is an element of the offense of making false statements in violation of § 1001, does apply retroactively. See Bilzerian, 127 F.3d at 242. The rule announced in Ali, we explained, was substantive, rather than procedural. While a new rule of constitutional criminal procedure generally does not apply retroactively on collateral review, a new rule of substantive criminal law is presumptively retroactive because a defendant may have been “punished for conduct that simply is not illegal.” Id.; see Ingber v. Enzor, 841 F.2d 450, 453-54 (2d Cir.1988). We determined that the rule in Ali presented such a case; that is, Ali redefined § 1001 “to legalize certain conduct previously thought to be criminal.” Bilzerian, 127 F.3d at 242. Accordingly, we held that the rule of Ali—that materiality is an element of the offense of making false statements in violation of § 1001— applies retroactively on collateral review. See id.11
B.
In Mandanici’s case, materiality was not an element of the false statements offenses with which he was charged, and which survived intact following direct appeal. Thus, at first glance, his case would appear to be an Aii-type case. Nevertheless, as Mandanici concedes, Judge Zampano made a finding of materiality as a matter of law. Accordingly, in ruling on the present petition, Judge Thompson treated Mandanici’s case as;.a Gaudin-type case and held, following Bilzerian, that the new procedural rale does not apply retroactively on collateral review.
On appeal, Mandanici challenges Judge Thompson’s conclusion on the ground that Judge Zampano erred not only in failing to submit the question of materiality to the jury, but also in the standard of proof he used to decide the question as a matter of law. Specifically, Mandanici argues that [526]*526(1) in accordance with Second Circuit law at the time, the issue of materiality was decided at his trial under a preponderance-of-the-evidence standard; (2) after Gaudin and Ali, materiality must be proved beyond a reasonable doubt; and (3) notwithstanding Bilzerian, this change in the law should be applied retroactively under Teague. We agree with the first two steps of this argument, but disagree with the third.
1.
First, we are persuaded that Judge Zampano decided the issue of materiality at Mandanici’s trial under the preponderance standard. The trial transcript itself does not make clear what standard Judge . Zampano used.12 However, to the extent that materiality was treated as an element of an offense when Mandaniei was tried, the law within this Circuit was that the judge decided the question as a matter of law under the preponderance standard. See, e.g., Gribben, 984 F.2d at 50-51 (stating that “[t]he government bears ... the burden of proving materiality [under both 18 U.S.C. § 1623(a) and the first clause of § 1001], but its burden need not be ‘beyond a reasonable doubt’; the burden is satisfied by a preponderance of the evidence ” (emphasis added)); United States v. Cunningham, 723 F.2d 217, 226 (2d Cir.1983) (“Materiality [under § 1623] is ordinarily to be determined by the court by a preponderance of the evidence.”).13 [527]*527Under these circumstances, we assume that Judge Zampano made his finding of materiality at Mandanici’s trial using the preponderance standard. Cf. Bilzerian, 127 F.3d at 240 (“A court in the Second Circuit, deciding the issue at the time of Bilzerian’s trial, would certainly have felt compelled to follow the existing precedent in its circuit”).
2.
Because it is plain that, after Gaudin and Ali, a finding of materiality under § 1001 must be made using the reasonable doubt standard,14 the next question is whether this change in the law applies retroactively on collateral review.15 Although we have never actually addressed the question of whether Teague applies to petitions for a writ of error coram nobis, we have stated that, “[b]e-cause of the similarities between coram nobis proceedings and § 2255 proceedings, the § 2255 procedure often is applied by analogy in coram nobis cases.” Fleming, 146 F.3d at 90 n. 2 (internal quotation marks omitted). Accordingly, we now hold that Teague applies to coram nobis petitions. See United States v. Swindall, 107 F.3d 831, 833-34 & n. 4 (11th Cir.1997) (applying Teague to a coram nobis petition); United States v. Nazon, 936 F.Supp. 563, 568-69 (N.D.Ind.1996) (same).
Under Teague, “new rules” of constitutional criminal procedure or novel applications of old rules “are generally not applied retroactively on [collateral] review.” Bilzerian, 127 F.3d at 240; see Stringer v. Black, 503 U.S. 222, 227-29, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992) (extending Teague to novel applications of old rules). A “new rule” is a rule that “breaks new ground or imposes a new obligation on the States or the Federal [528]*528Government.”. Teague, 489 U.S. at 301, 109 S.Ct. 1060 (plurality opinion). Put differently, “a case announces a new rule if the result was not dictated by precedent existing at the time the defendant’s conviction became final.” Id. Under these standards, the requirement that materiality under § 1001 be proved beyond a reasonable doubt is a new rule—or at least a novel application of an old rule. As we discussed above, prior to Gaudin and Ali, the law of this Circuit was that to the extent materiality was an element under § 1001, it posed a question of law for the trial judge to decide under a preponderance-of-the-evidence standard. See Gribben, 984 F.2d at 50-51; see also Gaudin, 515 U.S. at 510 n. 1, 115 S.Ct. 2310 (noting that “some courts,” including this Court and the Sixth Circuit, “do not require the higher burden of proof’). Thus, it cannot be said that a court considering Mandani-ci’s claim at the time his conviction became final “would have felt compelled by existing precedent to conclude” that the Constitution required proof of materiality beyond a reasonable doubt. Gray v. Netherland, 518 U.S. 152, 166, 116 S.Ct. 2074, 135 L.Ed.2d 457 (1996) (internal quotation marks omitted); see also Butler v. McKellar, 494 U.S. 407, 412, 110 S.Ct. 1212, 108 L.Ed.2d 347 (1990) (“A new decision that explicitly overrules an earlier holding obviously ‘breaks new ground’ or ‘imposes a new obligation.’ ”).
3.
Because the requirement that materiality be proved beyond a reasonable doubt for conviction under § 1001 is a new rule, it does not apply retroactively on collateral review unless it fits within one of the two Teague exceptions. Mandanici wisely concedes the inapplicability of the first Teague exception—for new rules that “place an entire category of primary conduct beyond the reach of the criminal law” or that “prohibit imposition of a certain type of punishment for a class of defendants because of their status or offense.” Sawyer, 497 U.S. at 241, 110 S.Ct. 2822. Instead, he argues that the change in the law to require proof of materiality beyond a reasonable doubt fits within the second Teag-ue exception. Although this question is a close one, we hold that the second Teague exception is also inapplicable.
The second Teague exception extends to new “watershed rules of criminal procedure implicating the fundamental fairness and accuracy of the criminal proceeding.” O’Dell v. Netherland, 521 U.S. 151, 167, 117 S.Ct. 1969, 138 L.Ed.2d 351 (1997) (internal quotation marks omitted). Although the Supreme Court has acknowledged that “the precise contours of this exception may be difficult to discern,” Saffle v. Parks, 494 U.S. 484, 495, 110 S.Ct. 1257, 108 L.Ed.2d 415 (1990), it has emphasized, through words and example, that the exception is exceedingly narrow, applying “only to a small core of rules requiring observance of those procedures that ... are implicit in the concept of ordered liberty,” Graham v. Collins, 506 U.S. 461, 478, 113 S.Ct. 892, 122 L.Ed.2d 260 (1993) (internal quotation marks omitted) (ellipsis in original). To fit within the second exception, it is not enough that a new rule “is aimed at improving the accuracy of trial,” Sawyer, 497 U.S. at 242, 110 S.Ct. 2822, or even that it promotes “[t]he objectives of fairness and accuracy,” Saffle, 494 U.S. at 495, 110 S.Ct. 1257. The new rule must also be a “watershed rule[ ]” that “alter[s] our understanding of the bedrock procedural elements essential to the fairness of a proceeding.” Sawyer, 497 U.S. at 241-42, 110 S.Ct. 2822 (internal quotation marks and emphasis omitted). In short, it must be a “groundbreaking occurrence,” Caspari v. Bohlen, 510 U.S. 383, 396, 114 S.Ct. 948, 127 L.Ed.2d 236 (1994), a “sweeping” change that applies to a large swathe of cases rather than a “narrow right” that applies only to a “limited class” of cases, O’Dell, 521 U.S. at 167, 117 S.Ct. 1969.
The Supreme Court has underscored the narrowness of the second Teague exception by invoking the “sweeping rule” of Gideon v. Wainwright, 372 U.S. 335, 83 [529]*529S.Ct. 792, 9 L.Ed.2d 799 (1963), as an example of the type of rule that fits within the exception, O’Dell, 521 U.S. at 167, 117 S.Ct. 1969; see Saffle, 494 U.S. at 495, 110 S.Ct. 1257 (stating that a rule must have “the primacy and centrality of the rule adopted in Gideon or other rules which may be thought to be within the exception” to quality under the second Teague exception); see also Gray, 518 U.S. at 170, 116 S.Ct. 2074, and by repeatedly noting that “we believe it unlikely that many such components of basic due process have yet to emerge.” Teague, 489 U.S. at 313, 109 S.Ct. 1060 (plurality opinion); accord Graham, 506 U.S. at 478, 113 S.Ct. 892; Sawyer, 497 U.S. at 243, 110 S.Ct. 2822; Butler, 494 U.S. at 416, 110 S.Ct. 1212. The Supreme Court has further underscored the narrowness of the second Teague exception by its example. Beginning with the rule at issue in Teagxle, the Court has measured at least eleven new rules, or proposed new rules, of criminal procedure against the criteria for the second exception and, in every case, has refused to apply the rale at issue retroactively. See O’Dell, 521 U.S. at 167, 117 S.Ct. 1969 (rule announced in Simmons v. South Carolina, 512 U.S. 154, 114 S.Ct. 2187, 129 L.Ed.2d 133 (1994), that a capital defendant must be permitted to inform his sentencing jury that he is parole-ineligible if the prosecution argues that he is a future danger); Lambrix v. Singletary, 520 U.S. 518, 539-40, 117 S.Ct. 1517, 137 L.Ed.2d 771 (1997) (rule announced in Espinosa v. Florida, 505 U.S. 1079, 112 S.Ct. 2926, 120 L.Ed.2d 854 (1992), that in certain states where a sentencing judge is required to give deference to a jury’s advisory sentencing recommendation with respect to the death penalty, neither the jury nor the judge is permitted to consider invalid aggravating circumstances); Gray, 518 U.S. at 170, 116 S.Ct. 2074 (rule that the state’s failure to give adequate notice of some of the evidence it intended to use in the petitioner’s capital sentence proceeding violates due process); Goeke v. Branch, 514 U.S. 115, 120-21, 115 S.Ct. 1275, 131 L.Ed.2d 152 (1995) (per curiam) (rule that due process generally prohibits a state appellate court from dismissing the appeal of a recaptured fugitive); Caspary 510 U.S. at 396, 114 S.Ct. 948 (rule that twice subjecting a defendant to a noncapital sentence enhancement proceeding violates the Double Jeopardy Clause); Gilmore v. Taylor, 508 U.S. 333, 345-46, 113 S.Ct. 2112, 124 L.Ed.2d 306 (1993) (rule announced in Falconer v. Lane, 905 F.2d 1129 (7th Cir.1990), that the failure to instruct a jury that it could not return a murder conviction if it found that the defendant possessed a mitigating mental state violates due process); Graham, 506 U.S. at 478, 113 S.Ct. 892 (proposed rale that jury instructions preventing a petitioner’s sentencing jury from considering mitigating evidence in a capital sentencing proceeding violate the petitioner’s Eighth and Fourteenth Amendment rights); Sawyer, 497 U.S. at 241-45, 110 S.Ct. 2822 (rule announced in Caldxuell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985), that the Eighth Amendment prohibits the imposition of a death sentence by a jury that has been led to the false belief that responsibility for determining the appropriateness of the capital sentence lies elsewhere); Saffle, 494 U.S. at 495, 110 S.Ct. 1257 (proposed rule that the trial court’s instruction in the petitioner’s capital sentence proceeding, telling the jury to “avoid any influence of sympathy,” violates the Eighth Amendment); Butler, 494 U.S. at 416, 110 S.Ct. 1212 (rule announced in Arizona v. Roberson, 486 U.S. 675, 108 S.Ct. 2093, 100 L.Ed.2d 704 (1988), that the Fifth Amendment bars police-initiated interrogation following a suspect’s request for counsel in the context of a separate investigation); Teague, 489 U.S. at 314-15, 109 S.Ct. 1060 (plurality opinion) (rule announced in Taylor v. Louisiana, 419 U.S. 522, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975), that the Sixth Amendment’s fair cross-section requirement, applies to a petit jury).
With these principles and examples in mind, we conclude that the rale requiring proof of materiality beyond a reasonable [530]*530doubt for conviction under § 1001 does not fit within the second Teague exception. To be sure, we agree with Mandanici that such a rule promotes both accuracy and fairness. See, e.g., In re Winship, 397 U.S. 358, 363, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970) (holding that the reasonable doubt standard is “a prime instrument for reducing the risk of convictions resting on factual error. The standard provides concrete substance for the presumption of innocence' — that bedrock axiomatic and elementary principle whose enforcement lies at the foundation of the administration of our criminal law.” (internal quotation marks omitted)); see also Sullivan v. Louisiana, 508 U.S. 275, 281, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993) (referring to the reasonable doubt requirement as “a ‘basic protectio[n]’ whose precise effects are unmeasurable, but without which a criminal trial cannot reliably serve its function” (alteration in original)); cf. Nutter v. White, 39 F.3d 1154, 1157-58 (11th Cir.1994) (holding that the rule announced in Cage v. Louisiana, 498 U.S. 39, 111 S.Ct. 328, 112 L.Ed.2d 339 (1990) (per curiam), that certain jury instructions on the beyond-a-reasonable-doubt standard violate due process, fits within the second Teague exception because “[t]he reasonable doubt standard guards against conviction of the innocent by ensuring the systematic accuracy of the criminal system” and an improper reasonable doubt charge “undermines the fundamental fairness of every trial in which it is used”). Moreover, we acknowledge that some cases, including at least one in this Circuit, can be read to hold that promoting fairness and accuracy is, by itself, sufficient to qualify for the second Teague exception. See Sanders v. Sullivan, 900 F.2d 601, 606-07 (2d Cir.1990) (holding that a rule prohibiting conviction based on the use of perjured testimony at trial even though the prosecution has no knowledge of its falsity qualifies for the second Teag-ue exception); see also Ostrosky v. Alaska, 913 F.2d 590, 594-95 (9th Cir.1990) (holding that a rule that a defendant has a due process right “to rely as a matter of law on a lower court decision in his own case that a statute is unconstitutional even though the case is on appeal to a higher court” fits within the second Teague exception). However, the Supreme Court has emphasized, most recently in O’Dell, that to qualify for the second Teague exception, a rule must also be a “watershed” rule. See O’Dell, 521 U.S. at 167, 117 S.Ct. 1969; see also Lyons v. Stovall, 188 F.3d 327, 341-42 (6th Cir.1999); Spaziano v. Singletary, 36 F.3d 1028, 1042-43 (11th Cir.1994); Cain v. Redman, 947 F.2d 817, 822 (6th Cir.1991). Indeed, in 1990, in Sawyer v. Smith, the Supreme Court explicitly rejected an argument made by the petitioner that “the second Teague exception should be read to include new rules ... that preserve ... accuracy and fairness,” 497 U.S. at 242, 110 S.Ct. 2822 (internal quotation marks omitted), admonishing that such a test
looks only to half of our definition of the second exception. Acceptance of petitioner’s argument would return the second exception to the broad definition that Justice Harlan first proposed in Desist, but later abandoned in Mackey [v. United States, 401 U.S. 667, 91 S.Ct. 1171, 28 L.Ed.2d 388 (1971)], under which new rules that “significantly improve the pre-existing fact-finding procedures are to be retroactively applied on habeas.” Desist v. United States, 394 U.S. 244, 262, 89 S.Ct. 1030, 22 L.Ed.2d 248 (1969). In Teague, we modified Justice Harlan’s test to combine the accuracy element of the Desist test with the Mackey limitation of the exception to watershed rules of fundamental fairness. It is thus not enough under Teague to say that a new rule is aimed at improving the accuracy of trial. More is required. A rule that qualifies under this exception must not only improve accuracy, but also “ ‘alter our understanding of the bedrock procedural elements ’ ” essential to the fairness of a proceeding. Teague, 489 U.S. at 311, [531]*531109 S.Ct. 1060 (quoting Mackey, 401 U.S. at 693, 91 S.Ct. 1171).
497 U.S. at 242, 110 S.Ct. 2822.
In short, unlike the “sweeping rule of Gideon, which established an affirmative right to counsel in all felony cases,” O’Dell, 521 U.S. at 167, 117 S.Ct. 1969, the requirement that materiality be proved beyond a reasonable doubt for conviction under § 1001 is a “narrow right” that affects only “a limited class” of cases, id. — indeed, as we discussed above, it affects only a subset of § 1001 cases, in the subset of circuits, like ours, that prior to Gaudin had allowed proof of materiality by a mere preponderance of the evidence. Thus, “[wjhatever one may think of the importance of [this] rule” — and we think it is of great importance — “it has none of the primacy and centrality of the rule adopted in Gideon or other rules which may be thought to be within the exception.” Saffle, 494 U.S. at 495, 110 S.Ct. 1257. Accordingly, the rule that materiality must be proved beyond a reasonable doubt for conviction under § 1001 does not apply retroactively on collateral review, and Mandanici cannot challenge his 1983 conviction on the basis of any such error.
III.
To summarize, we hold as follows:
(1) With respect to the offenses of making false statements in violation of 18 U.S.C. § 1001 of which Mandanici was convicted in 1983, and which survived intact following direct appeal, the trial judge made a finding of materiality using the preponderance-of-the-evidence standard, consistent (to the extent relevant here) with the law of this Circuit at the time of the trial.
(2) Following United States v. Gaudin, 515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995), and United States v. Ali, 68 F.3d 1468 (2d Cir.1995), the law in this Circuit requires that for a conviction under § 1001 to be sustained, the jury must have made a finding of materiality beyond a reasonable doubt.
(3) The framework established by the Supreme Court in Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), applies to petitions for a writ of error coram nobis.
(4) Under Teague, the change in the law of this Circuit to require a finding of materiality beyond a reasonable doubt in any and all prosecutions under § 1001 is a new rule of constitutional criminal procedure or a novel application of an old rule — and therefore does not apply retroactively unless it falls within one of the two exceptions fashioned by the Supreme Court.
(5) This change concededly does not fit within the first Teague exception, for new rules that “place an entire category of primary conduct beyond the reach of the criminal law, or new rules that prohibit imposition of a certain type of punishment for a class of defendants because of their status or offense.” Sawyer v. Smith, 497 U.S. 227, 241, 110 S.Ct. 2822, 111 L.Ed.2d 193 (1990) (citation omitted).
(6) Nor does this change fit within the second Teague exception, for “new ‘watershed rules of criminal procedure’ that are necessary to the fundamental fairness of the criminal proceeding.” Sawyer, 497 U.S. at 241-42, 110 S.Ct. 2822.
(7) Thus, the rule that materiality must be proved beyond a reasonable doubt for conviction under § 1001 does not apply retroactively on collateral review, and Mandanici cannot challenge his 1983 conviction on the ground of any such error.
Accordingly, the judgment of the District Court is affirmed.