
502 F.3d 122 (2007)
UNITED STATES of America, Appellant,
v.
Gregg BECKER, Defendant-Appellee.
Docket No. 06-1274-cr.
United States Court of Appeals, Second Circuit.
Argued: June 13, 2007.
Decided: September 13, 2007.
*123 *124 Joshua Klein, Assistant United States Attorney (Robin L. Baker, Assistant United States Attorney, on the brief) for Michael J. Garcia, United States Attorney for the Southern District of New York, New York, NY, for Appellant.
Maranda Fritz, Hinshaw & Culbertson LLP, New York, NY, for Defendant-Appellee.
Before: CALABRESI, B.D. PARKER, and WESLEY, Circuit Judges.
B.D. PARKER, Jr., Circuit Judge:
In 2002 the government charged Gregg Becker with one count of securities fraud and one count of conspiracy to commit securities fraud, mail fraud, and wire fraud. See 15 U.S.C. §§ 78j(b), 78ff; 17 C.F.R. § 240.10b-5; 18 U.S.C. § 371. After a jury trial in the United States District Court for the Southern District of New York (Patterson, J.), Becker was convicted on both the substantive and the conspiracy counts. Judge Patterson sentenced him to 24 months' imprisonment, followed by three years of supervised release.[1] Becker appealed his conviction to this Court, and we affirmed in an unpublished summary order filed October 31, 2003. We subsequently denied Becker's timely petition for rehearing on December 19, 2003.
On March 8, 2004, the Supreme Court decided Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004), which held that the Sixth Amendment's Confrontation Clause bars the admission of out-of-court testimonial statements unless the declarant is unavailable and the defendant has had a prior opportunity to cross-examine. See id. at 59, 124 S.Ct. 1354. Relying on Crawford, Becker petitioned for a writ of habeas corpus, contending that his Sixth Amendment right to confrontation had been violated by the district court's admission of eleven plea allocution transcripts of alleged co-conspirators. See 28 U.S.C. § 2255. Judge Patterson *125 granted Becker's petition, finding that under Crawford it was error to admit the plea allocutions and that this error was not harmless. Based on these findings, the court vacated Becker's conviction and ordered a new trial. The government appeals, contending that Becker's Crawford claim is procedurally barred and, alternatively, that any error in admitting the plea allocutions was harmless. We affirm.

BACKGROUND
From 1995 to 1996, Becker was employed as a licensed securities broker at the Melville, Long Island branch of Investor Associates ("IA"). It was later revealed that several IA brokers had been engaged in a massive securities fraud during this period. The Melville branch operated as a so-called "boiler room," where brokers were trained to cold call potential clients and pressure them into purchasing risky securities using a variety of deceptive sales tactics. In particular, brokers were instructed, and given incentives, to sell several highly speculative "house stocks" for which IA had participated in underwriting the initial public offerings. To generate interest from investors in the house stocks, IA brokers would follow sales scripts that contained false and misleading information about the stability of the securities and their potential for future growth. The brokers also lied to investors regarding their own backgrounds, level of experience in finance, and past performance. The demand created by these misrepresentations artificially inflated the share price of the house stocks, and the brokers collected large commissions. Meanwhile, investors were discouraged from selling the stocks, even as share prices inevitably fell and they experienced substantial losses.
At trial, the government presented several recorded telephone conversations in which Becker was heard lying to potential customers about his experience as a broker, his personal income and net worth, and the manner in which he was compensated for executing trades. On the recordings, Becker was also heard making predictions regarding the growth potential of house stocks and encouraging investors to hold their shares despite falling prices. In addition, the government presented the live testimony of Joseph Mandaro and Todd Peterson, two cooperating witnesses who were former IA brokers, and of three of Becker's former customers who had sustained significant monetary losses.
On direct examination, Mandaro testified to having told numerous lies to customers in connection with selling the house stocks. He further testified that he worked "very close with Gregg" and that much of the information that Becker gave to customers regarding his personal background and experience in the financial industry was false. Mandaro testified that he made similar false statements regarding his own background to give customers "the sense of a well-established well-known successful broker." About such statements, he testified: "I knew it was illegal. I knew it was a blatant lie." Peterson testified similarly regarding lies he told customers regarding his personal background, as well as about his understanding that such lies were inconsistent with the training he had completed to become a licensed securities broker. Both Mandaro and Peterson also testified that they lied to customers about the commissions they received on the sale of house stocks, about the length of time the customers could expect to hold the stocks before selling them, and about the likelihood that the house stocks would increase in value.
*126 Finally, the government read into evidence, over the defense's objections, the transcripts of eleven plea allocutions by former IA brokers who described their intentional participation in the fraudulent scheme. These plea allocutions  which the government no doubt anticipated, at the time they were taken, would be powerful evidence but not subject to cross-examination when introduced in a subsequent trial  went far beyond anything required by Rule 11 of the Federal Rules of Criminal Procedure. Each allocuting defendant discussed in detail the specific practices used to carry out the fraud at IA  especially the use of sales scripts to mislead customers into purchasing securities and the broker's inflation of his own credentials to further deceive customers  and these details were largely identical among the allocutions. The allocutions also contained broad statements concerning the pervasiveness of the fraud. For example: "It was well-known at Investors Associates that . . . you couldn't just let clients sell house stock." In addition, some defendants referred throughout their allocutions to actions "we" took  for example, "[w]e also used the high pressure sales tactics that was described in the charges"  potentially implying that all IA brokers were knowing participants in the conspiracy.
Prior to admitting the plea allocutions, the court instructed the jury that it could consider them "for proof that a conspiracy existed as charged in the indictment, but not to show that any defendant here was a member of that conspiracy." The court further instructed the jury to "consider these allocutions only for the following two issues: (1) there was a conspiracy or a scheme to commit securities fraud, mail fraud, or wire fraud; (2) what, if anything, each of the persons' testimonies you're about to hear did to further the object of the conspiracy, if you do find that a conspiracy existed." The court reiterated these limiting instructions immediately after the transcripts were read, emphasizing that "[t]here is no evidence in these statements that any of the defendants are co-conspirators." At the conclusion of the trial, the court again reminded the jury that it could "consider evidence that other people pleaded guilty to these crimes as evidence that a conspiracy existed" but could "not consider the guilty pleas of others as evidence that any of the defendants were members of the alleged conspiracy."
The jury found Becker guilty on both counts of the indictment. On direct appeal, we rejected Becker's arguments that the misrepresentations he made to investors regarding his background and experience were not material; that the misrepresentations were not made "in connection with" the purchase or sale of the house stocks; that the government failed to prove that Becker had the necessary intent to support a securities fraud conviction; and that the district court erred in admitting the plea allocutions as evidence of the charged conspiracy. As noted above, our summary order affirming the conviction was filed on October 31, 2003, and we denied Becker's petition for rehearing on December 19, 2003. Although Becker had until March 18, 2004  ten days after the Supreme Court decided Crawford  to file a timely petition for certiorari, see SUP.CT. R. 13(3), he did not do so.
Subsequently, Becker petitioned for habeas relief, pressing several arguments including that the admission of the plea allocutions violated Crawford. The district court denied the petition on all bases except the Crawford claim. United States v. Becker, No. 01 Cr. 156(RPP), 2005 WL 3110650, at *9-*10 (S.D.N.Y. Nov. 18, 2005) ("Becker I"). The court rejected the government's argument that Crawford was inapplicable, reasoning that under *127 Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), Becker's conviction did not become final until after Crawford was decided and, as a result, Crawford applied despite being non-retroactive. Id. at *9; see Mungo v. Duncan, 393 F.3d 327, 336 (2d Cir.2004). The court also determined that the admission of the plea allocutions violated Crawford. Becker I, at * 10. In a later opinion, the court held that the Crawford error was not harmless, and vacated the conviction and ordered a new trial. United States v. Becker, No. 01 Cr. 156(RPP), 2006 WL 156677 (S.D.N.Y. Jan. 17, 2006). This appeal followed.

DISCUSSION
We review a district court's decision to grant a habeas petition de novo and the court's factual findings for clear error. Hawkins v. Costello, 460 F.3d 238, 242 (2d Cir.2006); Campusano v. United States, 442 F.3d 770, 773 (2d Cir.2006).

I. Whether Becker's Crawford Claim Is Procedurally Barred
Initially, the government contends that because Becker challenged the admission of the plea allocutions on direct appeal and this Court affirmed his conviction, law of the case precludes him from again raising the issue on collateral review. "The law of the case ordinarily forecloses relitigation of issues expressly or impliedly decided by the appellate court." United States v. Quintieri, 306 F.3d 1217, 1229 (2d Cir.2002) (internal quotation marks omitted). Applying this general principle, we have held that "section 2255 may not be employed to relitigate questions which were raised and considered on direct appeal." Cabrera v. United States, 972 F.2d 23, 25 (2d Cir.1992) (internal quotation marks omitted). Nevertheless, application of the doctrine remains a matter of discretion, not jurisdiction. See United States v. Tenzer, 213 F.3d 34, 39 (2d Cir.2000) (observing that while law of the case "informs the court's discretion, [it] does not limit the tribunal's power" (internal quotation marks omitted)). We may find it appropriate to reconsider an earlier decision when we are confronted with "an intervening change of controlling law, the availability of new evidence, or the need to correct a clear error or prevent manifest injustice." Id. (internal quotation marks omitted); see also United States v. Thorn, 446 F.3d 378, 383 (2d Cir.2006); United States v. Loschiavo, 531 F.2d 659, 663-64 (2d Cir.1976).
In our prior decision rejecting Becker's direct appeal, we relied on the "well-settled" principle "that plea allocutions of unavailable co-conspirators are admissible at trial as statements against interest," and therefore fall within an exception to the hearsay rule. The Supreme Court uprooted that principle when it concluded that, "[w]here testimonial statements are involved, we do not think the Framers meant to leave the Sixth Amendment's protection to the vagaries of the rules of evidence." Crawford, 541 U.S. at 61, 124 S.Ct. 1354. Nevertheless, the government contends that Crawford did not represent an intervening change of law because when it was decided, Becker still had time to petition for certiorari.[2]
*128 We have never held that to establish an exception to the law of the case doctrine an intervening change of law must occur after a defendant's time to petition the Supreme Court for certiorari has expired. While we have not squarely addressed the issue, Supreme Court precedent points us toward an opposite conclusion from the one the government urges. Davis v. United States, 417 U.S. 333, 342, 94 S.Ct. 2298, 41 L.Ed.2d 109 (1974), held that law of the case did not preclude a petitioner from seeking § 2255 relief based on a change in the law that occurred after his conviction was affirmed on direct appeal. In Davis, the change resulted from a decision of the Ninth Circuit  the same court that had affirmed Davis's conviction on direct appeal  which was issued while Davis' certiorari petition was pending. The Supreme Court denied certiorari in the first instance, but granted review after Davis's subsequent § 2255 petition had been denied in the lower courts. Id. at 339-41, 94 S.Ct. 2298. In determining that Davis's habeas claim was not barred by the circuit court's decision on direct appeal, the Supreme Court implied that the result would be different had the change in law occurred while the defendant still had time to appeal his conviction but failed to do so. Id. at 345, 94 S.Ct. 2298 (discussing Sunal v. Large, 332 U.S. 174, 67 S.Ct. 1588, 91 L.Ed. 1982 (1947)). The Court did not, however, ascribe any significance to whether such a change occurred before or after the opportunity to petition for certiorari had expired.
The circumstances in Davis are directly analogous to those here insofar as the change of law on which Becker relies occurred after his direct appeal was decided but before his time to petition the Supreme Court for certiorari had expired. The fact that Davis actually filed a petition for certiorari, whereas Becker did not, is not dispositive. The rule the government advocates is that a change in law cannot be considered "intervening" if it occurs before a defendant's time to petition for certiorari expires, whether or not such a petition is filed. Such a rule would contradict Davis.
Moreover, the fact that the Supreme Court initially denied certiorari on Davis's direct appeal, before granting it on collateral review, demonstrates why the mere possibility of Supreme Court review is inadequate to prevent the "manifest injustice" that might result if a defendant in Davis's position, or in Becker's, were precluded from raising a change of law in a habeas petition. Although the government contends otherwise, we cannot predict with any certainty whether the Supreme Court, in any individual case, will grant the purely discretionary writ of certiorari. Pragmatism as well as precedent, therefore, supports our conclusion that an intervening change in law occurring after a defendant's direct appeal has been exhausted, but before his time to petition for certiorari has expired, may give rise to an exception to the law of the case doctrine on collateral review. We further conclude that such an exception is justified in this case, where the application of Crawford is necessary to "prevent manifest injustice." Tenzer, 213 F.3d at 39 (internal quotation marks omitted).
The government maintains that even if Crawford may be considered "intervening," it does not apply retroactively to Becker's case. This argument is based on a misreading of Teague v. Lane, in which the Supreme Court held that "[u]nless they fall within an exception to the general rule, new constitutional rules of criminal procedure will not be applicable to those cases which have become final before the *129 new rules are announced." 489 U.S. at 310, 109 S.Ct. 1060. Teague recognized two exceptions to the general rule of non-retroactivity: the first is for new rules that "place[] certain kinds of primary, private individual conduct beyond the power of the criminal law-making authority to proscribe," and the second is for new "watershed rules of criminal procedure." Id. at 311, 109 S.Ct. 1060 (internal quotation marks omitted). We have held that because the rule announced in Crawford does not fall within either exception to Teague, it "should not be applied retroactively on collateral review." Mungo, 393 F.3d at 336. The Supreme Court recently confirmed this understanding. Whorton v. Bockting, ___ U.S. ___, 127 S.Ct. 1173, 1184, 167 L.Ed.2d 1 (2007).
Were this a straightforward issue of retroactivity, there is no question that Becker's claim would be barred. Teague's rule of non-retroactivity, however, applies only "to those cases which have become final before the new rules are announced." Teague, 489 U.S. at 310, 109 S.Ct. 1060. In Mungo, we noted that "[a] conviction becomes final for the purposes of Teague when `the availability of direct appeal . . . has been exhausted and the time for filing a petition for a writ of certiorari has elapsed or a timely filed petition has been finally decided.'" Mungo, 393 F.3d at 333 n. 3 (quoting Beard v. Banks, 542 U.S. 406, 411, 124 S.Ct. 2504, 159 L.Ed.2d 494 (2004)). Timing was not an issue in Mungo because Crawford had been decided "long after . . . the date when petitioner's conviction became final." Id. at 334 n. 5. Here, Becker still had time to petition the Supreme Court for certiorari when Crawford was decided and, accordingly, his conviction had not become final for purposes of Teague. Non-retroactivity is therefore beside the point, and we turn to the merits of the government's appeal.

II. Crawford and Harmless Error Analysis
Prior to Crawford, we regularly approved the admission of an unavailable witness's plea allocution to prove the existence and scope of a conspiracy, and  so long as they were accompanied by particularized guarantees of trustworthiness  we rejected the argument that such statements violate the Confrontation Clause. See, e.g., United States v. Dolah, 245 F.3d 98, 104-05 (2d Cir.2001); United States v. Petrillo, 237 F.3d 119, 122-23 (2d Cir. 2000); United States v. Moskowitz, 215 F.3d 265, 269-70 (2d Cir.2000) (per curiam). Our approval was generally conditioned on the district court excluding from the plea allocutions any non-self-inculpatory statements before admitting them into evidence, as well as clearly limiting the jury's consideration of the allocutions to the issues of whether a conspiracy existed and what, if anything, the declarant did to further the objects of the conspiracy. See Petrillo, 237 F.3d at 123; Moskowitz, 215 F.3d at 268-69; see also United States v. Gallego, 191 F.3d 156, 167-68 (2d Cir. 1999).
In Crawford, the Supreme Court upended these precedents, and declared that the procedural safeguards we and other courts had relied on as guaranteeing the reliability of out-of-court testimonial statements were inadequate to compensate for the defendant's lack of an opportunity to cross-examine the declarant. See Crawford, 541 U.S. at 64-65, 124 S.Ct. 1354. "Where testimonial statements are at issue," the Supreme Court held, "the only indicium of reliability sufficient to satisfy constitutional demands is the one the Constitution actually prescribes: confrontation." Id. at 68-69, 124 S.Ct. 1354. We have since concluded that plea allocutions are testimonial, and are therefore subject *130 to the requirements set forth in Crawford. United States v. McClain, 377 F.3d 219, 221-22 (2d Cir.2004).
Whether or not the district court's decision to admit the plea allocutions in Becker's case was consistent with the then-controlling law of this Circuit, there can be no doubt after Crawford that their admission violated the Confrontation Clause. See id. at 222 ("[A] plea allocution by a co-conspirator who does not testify at trial may not be introduced as substantive evidence against a defendant unless the co-conspirator is unavailable and there has been a prior opportunity for cross-examination."). Thus, as the government essentially concedes, the district court's admission of the plea allocutions was constitutional error.[3]
Not every such error, however, necessitates a new trial. After Crawford, as before, we review Confrontation Clause violations under a harmless error standard. See United States v. Gotti, 459 F.3d 296, 343 (2d Cir.2006); United States v. Reifler, 446 F.3d 65, 87 (2d Cir.2006). To establish harmlessness, it is the government's burden to prove "beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained." McClain, 377 F.3d at 222 (internal quotation marks omitted). The government argues that the admission of the plea allocutions was harmless (a) because the jury is presumed to have followed the district court's limiting instructions, and (b) because there was overwhelming evidence of Becker's guilt. We disagree.

A. Limiting Instructions

The district court instructed the jury that it could consider the plea allocutions "only for the following two issues: (1) there was a conspiracy or a scheme to commit securities fraud, mail fraud, or wire fraud; (2) what, if anything, each of the persons' testimonies you're about to hear did to further the object of the conspiracy, if you do find that a conspiracy existed." The court added that "[t]here is no evidence in these statements that any of the defendants are co-conspirators," and reiterated its instructions at the conclusion of trial. The government contends that these limiting instructions were sufficient to render any Crawford error harmless beyond a reasonable doubt.
Generally, we presume that juries follow limiting instructions. See, e.g., United States v. Downing, 297 F.3d 52, 59 (2d Cir.2002); United States v. Salameh, 152 F.3d 88, 116 (2d Cir.1998). However, the presumption is overcome "where there is an overwhelming probability that the jury will be unable to follow the court's instructions and the evidence is devastating to the defense." United States v. Jones, 16 F.3d 487, 493 (2d Cir.1994) (citing Greer v. Miller, 483 U.S. 756, 766 n. 8, 107 S.Ct. 3102, 97 L.Ed.2d 618 (1987)). Stated another way, we have found it inappropriate to presume that a district court's *131 limiting instructions were obeyed when such instructions required jurors to perform "mental acrobatics." Id.; see also United States v. McDermott, 245 F.3d 133, 140 (2d Cir.2001) ("Although the district court here provided the jury with standard limiting instructions, we find that under the circumstances of the case, where the prejudicial spillover was so overwhelming, they cannot be presumed to be effective."); United States v. Colombo, 909 F.2d 711, 715 (2d Cir.1990) (finding an overwhelming probability that, despite limiting instructions, the jury was unable to dispassionately consider evidence of rape and sodomy admitted as "background" in a trial for RICO conspiracy and narcotics violations).
The government suggests that the present case is indistinguishable from United States v. Snype, 441 F.3d 119 (2d Cir. 2006). On direct appeal from a conviction for conspiracy to commit bank robbery, the defendant in Snype argued that the admission at trial of a co-conspirator's plea allocution constituted reversible error under Crawford (which was decided after the guilty verdict but before sentencing). Id. at 125, 128. We observed that the district court "carefully instructed the jury that it could consider [the plea] allocution only on two issues"  whether there was a conspiracy and what, if anything, the declarant did to further the objects of the conspiracy. Id. at 128. The court also "specifically instructed the jury that [the] allocution could not be used to determine Snype's membership in the charged conspiracy." Id. The court went on to note that Snype's membership "is an issue that you will have to decide based on other evidence," pointing out that the plea allocution did not name Snype, and emphasized that the jury's determination on this issue must not be based on statements in the allocution. Id.
We held, in light of Crawford, that it was error for the district court to admit the plea allocution, but concluded that such error was harmless beyond a reasonable doubt. Id. at 128, 130. Snype had "essentially conceded the existence of the charged conspiracy." Id. at 129. As to his assertion that "the jurors `could' have used [the] allocution for a second, impermissible purpose"  by inferring, despite the court's limiting instructions, that Snype was the "man" referred to in the statements of his alleged co-conspirator  we found that "it is Snype who proposes mental acrobatics." Id. at 129-30. Accordingly, we saw no reason to deviate from our general presumption that the jury had followed the limiting instructions. Id. at 130.
Here, as in Snype, Becker essentially concedes the existence of the charged conspiracy; he offered to stipulate to it at trial. However, ample grounds exist for distinguishing this case from Snype. First, the sheer number of plea allocutions admitted to prove the conspiracy in this case is significant, and highlights the importance of such testimony to the government's case. The number and repetitive nature of the allocutions also suggested that the conspiracy was widespread  making it plausible for the jury to assume that Becker was a participant simply by association with his co-workers.
Moreover, the content of the plea allocutions was unusually far-reaching and detailed, and touched directly on issues that were central to Becker's defense. To establish that Becker committed a criminal securities fraud violation, as well as to establish his membership in the conspiracy, the government was required to prove that he acted willfully. United States v. Cassese, 428 F.3d 92, 98 (2d Cir.2005); see also United States v. Aleskerova, 300 F.3d 286, 292 (2d Cir.2002) ("To establish membership *132 in a conspiracy, the government must prove that the defendant knowingly engaged in the conspiracy with the specific intent to commit the offenses that were the objects of the conspiracy." (internal quotation marks omitted)). We have defined willfulness in this context as "`a realization on the defendant's part that he was doing a wrongful act' under the securities laws." Cassese, 428 F.3d at 98 (quoting United States v. Peltz, 433 F.2d 48, 55 (2d Cir. 1970)).
At trial, Becker's primary defense to both counts of the indictment was that he lacked mental culpability, and that his actions as a broker at IA were driven by credulity and inexperience rather than by greed. This theory was bolstered by the facts that Becker was only nineteen years old when he began working at IA and that he left the firm within a year, purportedly upon realizing that his fellow brokers were engaged in illegal activity.
The plea allocutions significantly undermined this defense by suggesting that at least eleven other IA brokers had knowingly and willfully misled investors. The plea allocutions covered not only what each individual broker did to further the objects of the conspiracy, but also the knowledge and intent with which each engaged in fraudulent acts identical to those that Becker allegedly committed. The brokers, for example, testified that they deliberately inflated their levels of experience when talking to customers, pressured customers into buying the house stocks then actively discouraged them from selling those stocks, and made baseless predictions regarding future performance. Several brokers testified that they were in their early twenties and, like Becker, had little or no experience in finance when they began working at IA. Each admitted that he knew his acts were wrongful or illegal at the time he committed them. It would require no great leap in reasoning for a juror to assume that Becker's intent in misrepresenting to customers the value of the house stocks, as well as his own background and experience, matched that of the eleven other IA brokers who pled guilty to the same or similar conduct.
We do not have a great deal of difficulty concluding that, by introducing the allocutions, the government was inviting the jury to make precisely that improper assumption regarding Becker's criminal intent. For example, the Assistant United States Attorney argued to the court below that the plea allocutions would help rebut the defense's position that only a few brokers at the firm were engaging in intentional securities fraud because, "[i]f there's ten or 12 allocutions admitted, obviously this shows it was not some isolated conspiracy." In addition, the government's attorney placed great emphasis on the plea allocutions in his closing. Although he reiterated to the jury the district judge's limiting instruction, he described almost in the same breath how the eleven co-conspirators who pleaded guilty told exactly the same lies to investors as Becker allegedly had. In doing so, the government gutted the limiting instruction it now relies on to prove harmlessness. Cf. Jones, 16 F.3d at 492-93 ("In the course of giving th[e] limiting instruction, the [trial] judge reminded the jurors repeatedly that Jones was a convicted felon as he simultaneously asked them to put this consideration out of their minds when deciding if [witnesses] had identified the right man.").
In light of the plea allocutions' sweeping content and number, as well as their centrality to the government's case, we conclude that the limiting instruction given by the district court was too vague and too general to achieve its intended effect. In Snype, the limiting instruction expressly forbade jurors from drawing the impermissible *133 conclusion as to identity that the defendant suggested they nonetheless might have drawn. See Snype, 441 F.3d at 128. Here, by contrast, the court's instruction said nothing whatever about the crucial issue of Becker's criminal intent. That omission seems to us especially significant given the detailed manner in which the allocuting defendants testified regarding their own intent.
The government asserts that it was sufficient for the district court to exhort jurors not to consider the plea allocutions as evidence that Becker was a member of the conspiracy. In addition, because the jury was permitted to consider the allocutions "only" as to the two issues identified by the district court  existence of the conspiracy and what if anything each declarant did to further its objects  the government suggests that jurors were forbidden, by negative implication, from making inferences about Becker's intent or from considering the allocutions at all with regard to the substantive securities fraud count. Neither argument is convincing.
Precisely because the presumption that juries follow limiting instructions is a strong one, it is imperative that such instructions be clear and unequivocal. The district court explicitly instructed jurors not to consider the plea allocutions as proof of Becker's membership in the conspiracy, but did not mention other forbidden purposes. As a result, a reasonable juror might have assumed that she was permitted to consider the allocutions as to Becker's intent to commit securities fraud. Likewise, the court's instruction that jurors must rely "entirely on the other evidence in the case" to find that Becker was a member of the alleged conspiracy left open the possibility that they might rely on the plea allocutions to find that Becker intended to defraud investors. The fact that the court prefaced the permissible purposes for which the jury could consider the allocutions with the qualifier "only" does not negate this possibility. Given these ambiguities, we find that application of the presumption that the jury followed the court's limiting instructions in this case is not sufficient to prove harmlessness beyond a reasonable doubt. We are left with serious doubts as to what the instructions might have meant to any individual juror.
Even assuming that the district court's limiting instructions did, as the government suggests, imply that the plea allocutions could not be considered for any purpose other than Becker's membership in the conspiracy, we conclude that it would be "quixotic" to expect jurors to follow them. Cf. Jones, 16 F.3d at 493. When faced with the guilty pleas of eleven alleged co-conspirators  each of whom, like Becker, was a broker at IA, and each of whom confessed to intentionally defrauding investors using the same deceptive sales tactics  there was an overwhelming probability that the jurors would infer that Becker was simply no different from his former colleagues. That evidence was undoubtedly "devastating" to Becker's defense, which rested almost entirely on the proposition that, despite misleading customers in certain respects, he did not intend to commit fraud. Under these conditions, the presumption we ordinarily apply to a district court's limiting instructions collapses.

B. Other Evidence of Becker's Guilt

As an alternative basis for demonstrating harmless error, the government asserts that there was overwhelming evidence of Becker's guilt independent of the plea allocutions. Because it was error to admit the allocutions, the government must show not merely that the other evidence it presented at trial was sufficient to support a finding that Becker acted willfully, *134 but that it was so overwhelming as to convince us that the error was harmless beyond a reasonable doubt. See, e.g., McClain, 377 F.3d at 222. In assessing a Crawford error's likely impact, we generally consider a variety of factors, including "the strength of the government's case, the degree to which the statement was material to a critical issue, the extent to which the statement was cumulative, and the degree to which the government emphasized the erroneously admitted evidence in its presentation of the case." Reifler, 446 F.3d at 87. On the basis of these factors, we conclude that the government has failed to carry its weighty burden here.
Contrary to the government's contention, the other evidence presented with regard to Becker's criminal intent and his membership in the conspiracy was far from overwhelming. Beyond the plea allocutions, the government relied primarily on two sources of evidence to prove that Becker knew his actions in connection with the sale of house stocks violated the securities laws: Becker's own conduct, including the lies he told to customers regarding his background, experience, and compensation; and the testimony of Joseph Mandaro and Todd Peterson, the two cooperating witnesses.
Despite the recordings of Becker's conversations with customers and the testimony of the alleged victims who were misled into purchasing the house stocks, there was no direct evidence that Becker knew his actions were wrong or that he intended to defraud investors. Instead, the government suggests that the fact that Becker was a licensed securities broker implies that he must have known that what he was doing was wrongful because it was in violation of the fiduciary duty he owed to his customers. In presenting this argument to the jury, the prosecutor relied mainly on "what Joe Mandaro said. . . . That [fiduciary duty] means you have to look out for the best interests of the customers. He knows it's illegal to lie to the customers to get their money and hold it."
At trial, as well as on appeal, the government contended that Becker's actions were consistent with conduct that Mandaro and Peterson testified they engaged in knowingly as part of a scheme to defraud investors. For example, in his closing, the government's attorney pointed out that Becker and Mandaro were "peers. They're friends. . . . Becker must have known what Mandaro was all about and if they're working together it probably means Gregg Becker also thought that way[.] You know Gregg Becker lied about a bunch of things, working with Joe Mandaro."
The jury, however, had substantial reasons to doubt the credibility of both government witnesses. As the district court pointed out, both Peterson and Mandaro acknowledged that they faced significant prison terms for their roles in the conspiracy and were hoping to receive non-jail sentences in exchange for their testimony. Both admitted to having used illegal drugs on a regular basis. In addition, Mandaro admitted that he had lied under oath in proceedings before the National Association of Securities Dealers, and Peterson acknowledged having pled guilty to lying to postal inspectors.
Furthermore, on cross-examination Peterson acknowledged that he knew nothing about Becker's sales practices or other activities at the firm. Rather than relying on personal knowledge about what Becker did at IA, Peterson testified that he could "only go by what happened on, you know, the majority of the time. I mean, these were the practices at the firm, you know." Mandaro admitted on cross-examination that it took him up to six months to realize *135 that the practices IA brokers used to discourage customers from selling the house stocks were wrongful, despite having had greater experience in the financial industry than Becker. He also acknowledged that the firm distributed and required brokers to follow "scripts" for "absolutely everything," including opening customer accounts and selling the house stocks. Moreover, he acknowledged that the principals who oversaw the fraud at IA's Melville branch, Vincent Grieco and Douglas Mangan, were perceived to be well-connected, successful businessmen who had significant influence over the younger brokers.
All these facts elicited on cross-examination tended to support the defense's contention that Becker, due to his relative inexperience and naivete at the time he joined IA, may have lacked the criminal intent necessary to support a conviction for securities fraud. The defense had no similar opportunity at trial or before to cross-examine the eleven alleged co-conspirators whose plea allocutions the government read into evidence. It appears, therefore, that Becker suffered precisely the harm that the Confrontation Clause is intended to avoid. See, e.g., Lee v. Illinois, 476 U.S. 530, 541, 106 S.Ct. 2056, 90 L.Ed.2d 514 (1986) (recognizing that the "truthfinding function of the Confrontation Clause is uniquely threatened when an accomplice's confession is sought to be introduced against a criminal defendant without the benefit of cross-examination").
Far from being merely cumulative, the testimony of eleven other brokers admitting that they engaged in substantially the same conduct as Mandaro and Peterson, with the same level of awareness that their acts were wrong, was of critical importance to the government's case. Cf. McClain, 377 F.3d at 223. At a minimum, the allocutions bolstered Mandaro's and Peterson's otherwise uncorroborated statements that the knowing use of fraudulent sales tactics was widespread throughout the firm, and helped rebut the defense's attempts to undermine the credibility of the two live witnesses. In addition, the government's introduction of eleven plea allocutions made it substantially more difficult for the defense to differentiate Becker's intent from that of other brokers at the firm who had admitted to being members of the conspiracy. In his closing, the Assistant United States Attorney repeatedly highlighted the significance of the allocutions, and pointed out (at least by implication) their consistency with Mandaro's and Peterson's testimony.
The government contends, finally, that Becker is foreclosed from arguing a lack of criminal intent on habeas review because on direct appeal this Court concluded that the government's evidence as to intent was sufficient to support the jury's verdict. This argument confuses the applicable standard of review. As we have already noted, to overcome a Crawford error the government must prove more than mere sufficiency of the evidence it presented at trial. It must establish beyond a reasonable doubt that the erroneously admitted evidence did not affect the verdict obtained. Given the relative weaknesses in the testimony of Mandaro and Peterson, on which the government now relies as independent proof of Becker's criminal intent, it is disingenuous to suggest that the effect of the eleven erroneously admitted plea allocutions was entirely innocuous.
We need not and do not conclude that the result of Becker's trial necessarily would have been different had the district court excluded the plea allocutions from evidence. We do conclude, however, that the allocutions may well have influenced the jury's verdict. Because the other evidence of Becker's guilt was by no means *136 overwhelming, the government has failed to establish that the Crawford error was harmless beyond a reasonable doubt.

CONCLUSION
For the foregoing reasons, we affirm the judgment of the district court.
NOTES
[1]  Becker finished serving his prison sentence in October 2005. There remains a live case or controversy due to the collateral consequences that attach to criminal conviction post-release. See Perez v. Greiner, 296 F.3d 123, 125 (2d Cir.2002).
[2]  Supreme Court Rule 13 requires that a petition for a writ of certiorari be filed within 90 days after the entry of judgment by a court of appeals. "[I]f a petition for rehearing is timely filed in the lower court by any party, . . . the time to file the petition for a writ of certiorari for all parties . . . runs from the date of the denial of rehearing. . . ." SUP.CT. R. 13(3). As we have already noted, we denied Becker's petition for rehearing on December 19, 2003. Thus, by the time the Supreme Court decided Crawford on March 8, 2004, Becker had ten remaining days to file a timely petition for certiorari.
[3]  The government suggests in its brief that, as to the substantive count of the indictment, it was not even error for the district court to admit the plea allocutions because the court limited the jury's consideration of the allocutions to the conspiracy count. This argument is specious. The government does not contend, nor could it, that it would have been permissible under Crawford for the district court to admit the plea allocutions as proof under either count of the indictment against Becker. It perforce concedes that the admission of the allocutions was error. Given that concession, any argument regarding the purposes for which the jury might or might not have actually considered the allocutions necessarily goes to whether such error was harmless, not whether it existed at all. We address below the effectiveness of the district court's limiting instructions in the context of our harmless error analysis.
