
624 F.3d 1031 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Robert Sherman BERRY, Defendant-Appellant.
No. 08-35002.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted January 11, 2010.
Filed October 22, 2010.
*1032 Thomas O. Rice, Assistant United States Attorney, Spokane, WA, for the plaintiff-appellee.
Dan B. Johnson, Spokane, WA, for the defendant-appellant.
*1033 Before: ANDREW J. KLEINFELD, A. WALLACE TASHIMA, and RICHARD C. TALLMAN, Circuit Judges.

OPINION
TASHIMA, Circuit Judge:
In 2007, almost ten years after he was convicted of two bank robberies, three bombings, and a number of related charges, Robert Berry filed a motion to vacate his conviction under 28 U.S.C. § 2255. Although purportedly brought under § 2255, Berry's motion largely sought the substantive relief of a motion for a new trial under Federal Rule of Criminal Procedure 33. Because Berrywho proceeded before the district court pro semislabeled his claims in this fashion, neither the government nor the district court noticed that the claims were barred by Rule 33's three-year limitation. See Fed.R.Crim.P. 33(b)(1). Instead, following our instruction in United States v. Jackson, 209 F.3d 1103 (9th Cir.2000), the district court treated Berry's mislabeled § 2255 motion "as a motion for a new trial," id. at 1106, and proceeded to deny the motion on the merits.
Obviously, the end result of the district court proceedings made little sense: Berry was effectively allowed to bring a new trial motion despite the fact that the deadline for such a motion had expired seven years earlier. In light of this anomalous result, we take this opportunity to clarify our prior decision. Jackson allows a district court to treat a § 2255 motion as a motion for a new trial under Rule 33. Generally, the district court may do so only when the prisoner brings his § 2255 motion within the time period established by Rule 33. However, when the prisoner's § 2255 motion falls outside this time period, the district court may still treat it as a Rule 33 motion if the government waives any objection to Rule 33 timeliness.
Under this standard, Berry's motion was well out of time. Nevertheless, because the government failed to object to the timeliness of Berry's new trial claims, the district court properly reached the merits of those claims. On the merits, we conclude that the district court correctly rejected Berry's contention that he is entitled to a new trial.

I. FACTUAL AND PROCEDURAL BACKGROUND
Before his conviction, Berry was a resident of Sandpoint, a small town in northern Idaho. Sandpoint lies only thirty miles from Ruby Ridge, the site of an infamous FBI standoff in 1992. Berry, along with his codefendants Charles Barbee and Verne Merrell, were deeply affected by the tragic events at Ruby Ridge. Already distrustful of government, the three became increasingly extremist in their views. Professing their belief in the need for a citizen militia, they started stockpiling weapons, stopped paying taxes, and began cash-only subsistence lifestyles in an attempt to go "off the grid."
None of the three, however, succeeded in staying off the grid for long. In 1996, the government indicted Berry, Barbee, and Merrell on charges stemming from three bombings and two bank robberies in Spokane, Washington, and an apparent attempt at a third bank robbery in Portland, Oregon. The three were eventually convicted of all charges against them.
Ten years later, Berry filed a motion under 28 U.S.C. § 2255, seeking to have his conviction overturned based on new information he learned about the forensic evidence the government used against him. The district court denied the motion, and we issued a certificate of appealability on the question whether the new evidence entitled Berry to a new trial.


*1034 A. The Bank Robberies

At approximately 2:30 p.m. on April 1, 1996, a pipe bomb went off outside the office of The Spokesman Review newspaper in Spokane. Shortly after the bombing, two masked men entered a U.S. Bank branch located a few blocks away. The men stole approximately $72,000 and detonated a second pipe bomb inside the bank before fleeing the scene.
At both The Spokesman Review and the U.S. Bank, the men left identical letters. The letters, written in a distinctive and archaic style, contained numerous religious references and were marked at the end with the symbol of the Phineas Priesthood.[1] The police later found a stolen van that they believed to have been used in both the bombing and the robbery, but were unable to determine who had committed the crimes.
Just over three months later, on July 12, 1996, another pipe bomb was set off in Spokane, this time outside the local office of Planned Parenthood. Shortly thereafter, three masked men entered the same U.S. Bank branch that had been robbed in April. This time, the men made off with $33,000.
At the Planned Parenthood bombing site, the police found a box of matches that contained religious markings similar to those found at the first bombing and bank robbery. The matchbox had handwritten citations to Psalms 139 and 127, a handdrawn symbol of the Phineas Priesthood, and the words "Praise Yahweh." As before, the police found a stolen van that was apparently used in the crime, but were unable to determine who committed the robbery.
After the second robbery, rewards ultimately totaling $130,000 were offered by U.S. Bank, The Spokesman Review, and the government for information leading to the arrest of the bank robbers. The reward prompted Christopher Davidson, a friend of Berry and owner of a military surplus business, to come forward. Davidson told the FBI that he believed Berry, Barbee, and Merrell were involved in the robberies.[2]
Based on Davidson's information, the FBI placed the trio under surveillance. On October 7, 1996, they watched Berry travel with Barbee and Merrell from Sandpoint to Portland, Oregon. In Portland, the three parked near a U.S. Bank and waited for it to open. The bank, on alert from the FBI, remained closed. After waiting outside the bank for 20 to 30 minutes, the three men left and drove to Union Gap, Washington, where they were arrested when they stopped to refuel.
Each of the defendants had been driving a separate vehicle at the time they were arrested, two of which were stolen. Inside these vehicles the FBI found a number of firearms, grenades, and ammunition. The FBI also found copies of a letter addressed to "the USurer Bank," written in the same style as the letters left behind in the other robberies. It was later learned that the defendants had mailed copies of this letter *1035 to The Spokesman Review, the Oregonian, and others.
Searches of the three defendants' residences revealed numerous other items that were potentially connected to the robberies. For example, Barbee's home contained Coleman propane canisters. Identical canisters had been found in a failed incendiary device left behind in the van used for the July 12 robbery. The FBI also found jeans in Barbee's bedroom that appeared to match jeans worn by one of the robbers in the April 1 robbery. And, in the headboard to Barbee's bed, they found a book entitled Vigilantes of Christendom: The Story of the Phineas Priesthood.
In Merrell's home, the FBI found a stun gun that matched one carried by one of the robbers in the July 12 robbery, as shown by a security video. They also found fuses in Merrell's van that were consistent with the fuses used in the pipe bombs. In addition, witnesses identified Merrell as the driver of the van in both the April 1 and July 12 robberies. Finally, files found on Merrell's home computer held contents substantially similar to the contents of letters left at U.S. Bank and outside The Spokesman Review office.
The FBI did not find any physical evidence in Berry's home that linked him to the robbery. They were, however, able to link him to the weapons used in the robberies. Photos from the robbery showed the robbers using what appeared to be a Benelli shotgun, a Winchester shotgun, and a Ruger Vaquero. Berry admitting to owning all three of these guns prior to the robberies, although he claimed to have sold them before the robberies occurred.

B. The Trial

Berry, Barbee, and Merrell were indicted and tried together in 1997. At their trial, in addition to the evidence summarized above, the government introduced the results of "compositional analysis of bullet lead" ("CABL") tests. CABL is a forensic technique that uses the chemical composition of lead to match bullets used in crimes with unfired bullets found in the possession of a criminal defendant. See generally Comm. on Sci. Assessment of Bullet Lead Elemental Composition Comparison, Nat'l Res. Council, Forensic Analysis: Weighing Bullet Lead Evidence 1-2 (2004), available at http://www.nap.edu/ catalog.php?record_id=10924# toc. Under the theory that the blocks of lead from which bullets are made are both unique in chemical composition and homogenous,[3] CABL purports to be able to determine if two bullets came from the same source. According to the government, if a bullet used in a crime is determined to have the same lead composition as an unfired bullet connected to a defendant, the defendant was more likely to have obtained both bullets from the same box of ammunition.
In Berry's case, the government used CABL tests to compare buckshot used in the Planned Parenthood pipe bomb with buckshot found in Berry's auto shop. Kathleen Lundy, a forensic examiner formerly with the FBI, testified that the buckshot pellets found at the two locations were chemically "indistinguishable," suggesting *1036 that both sets of buckshot came from the same source.
Additional evidence greatly strengthened the connection between Berry's buckshot and the buckshot recovered from the pipe bomb. To begin with, the label on the bag of buckshot found in Berry's shop indicated that it came from Hornaday Manufacturing Company. In her research, Lundy learned that Hornaday purchases its lead from a single supplier. Until 1996, that supplier had been Asarco. In early 1996, however, Hornaday had started purchasing lead exclusively from Doe Run. Because the chemical composition of the buckshot used in the Planned Parenthood bomb did not match the composition of either Asarco or Doe Run lead, Lundy believed that the buckshot had been created in 1996, during a time when Hornaday was using lead from both suppliers in its products.
Gregory Hanson, Director of Sales for Hornaday, confirmed much of Lundy's analysis. He testified that Hornaday had created a batch of 436 bags of buckshot from a mixture of Asarco and Doe Run lead in early 1996. In addition, Hanson testified that Hornaday was the only buckshot manufacturer who used bullets that were 3 percent antimony, a metal used to harden lead. Both the pipe-bomb buckshot and the buckshot in Berry's auto shop were 3 percent antimony, strongly suggesting that both came from the batch of buckshot that Hornaday manufactured in 1996. Of this batch, only thirty-two bags were shipped to the area of Spokane, Washington, and Coeur d'Alene, Idaho.
The end result of the CABL evidence was compelling. Between Lundy's and Hanson's testimony, the government narrowed the likely source of the buckshot in the Planned Parenthood pipe bomb to thirty-two bags, two of which were in Berry's possession.
In response to the government's evidence, Berry, Barbee, and Merrell all claimed that they were being framed by Davidson. They testified that the Portland trip was a copycat "media stunt" intended to draw publicity to what they saw as violations of "God's law." As part of the media stunt, Berry planned on running into the Portland bank in a trash bag, hood, and goggles, saying, "You have been served," delivering the letter found in the van, and leaving. Barbee's role was to hold the door for him, then set off a tear gas grenade. Merrell would act as the getaway driver. The three also disclaimed any intention to use in their supposed media stunt the firearms that they possessed at the time of their arrest. Instead, they claimed that the weaponry was part of the militia gear that they carried everywhere.
After trial, Berry, Barbee, and Merrell were convicted of the bombings and the bank robberies. On appeal, we affirmed their convictions. See Merrell, 1999 WL 386651.

C. The New Evidence

In 2006, Berry learned of two developments relating to the CABL evidence used to obtain his conviction. First, Berry learned that Lundy had later pleaded guilty to making a false statement in a Daubert[4] hearing in Kentucky state court in 2002. The facts of that matter, as set forth in Ragland v. Commonwealth, 191 S.W.3d 569 (Ky.2006), indicate that Lundy was called upon to testify that the bullet used in a murder was "analytically indistinguishable" from a bullet found in the defendant's possession. Id. at 574. According to her testimony, both bullets likely came from the same source, which she *1037 believed to be the Winchester Ammunition Company. Id.
Lundy's opinion was made more significant because she testified that the bullets came from lead that had been remelted by Winchester, as opposed to lead purchased in "billet" form, which can be directly converted into bullets without remelting. Id. at 575, 580. Because billets are generally created from a single, very large batch of lead, the fact that Winchester remelted its lead would have "substantially reduce[d] the number of possible bullets traceable to a particular `last melt.'" Id. at 580.
At the Daubert hearing, Lundy testified that Winchester remelted all the lead it obtained from its suppliers until 1996, when she knew that as early as 1986 it did not remelt some of its lead. Id. at 580-81. Because the murder had occurred in 1994, Lundy's false statement made the CABL evidence provide a stronger link between the defendant and the murder. Lundy eventually pled guilty to misdemeanor charges of false swearing. Id. at 581.
Second, Berry learned that the FBI had discontinued the use of CABL evidence at trials. Based on persistent criticism of CABL evidence, the FBI commissioned the National Research Council to evaluate the technique. The 2004 report that followed was critical of some of the FBI's practices. In particular, the report noted that the FBI was overstating some of the conclusions that could be drawn from CABL evidence. See Nat'l Res. Council, supra, at 6-7. Based on the results of the study, the FBI announced in 2005 that it would stop using CABL evidence in prosecutions. Since that time, a number of courts, including the Kentucky Supreme Court in Ragland, have overturned convictions that were based upon CABL evidence. See, e.g., Ragland, 191 S.W.3d at 581-82 (reversing conviction because "[the expert's] opinions based on CBLA evidence [did] not satisfy the reliability requirements of Daubert/Kumho"); see also Clemons v. State, 392 Md. 339, 896 A.2d 1059, 1078 (2006) ("Based on the criticism of the processes and assumptions underlying [CABL], we determine that the trial court erred in admitting expert testimony based on [CABL] because of the lack of general acceptance of the process in the scientific community."); State v. Behn, 375 N.J.Super. 409, 868 A.2d 329, 345-46 (2005) (reversing conviction based in part on CABL evidence); United States v. Mikos, 2003 WL 22922197, at *6 (N.D.Ill. Dec. 9, 2003), (excluding CABL evidence because "[t]here is no body of data to corroborate the government's expert's . . . opinion that [analytically indistinguishable] bullets must or even likely came from the same batch or melt").

D. The Motion

Armed with these two new developments, Berry filed a pro se motion under 28 U.S.C. § 2255 on July 2, 2007. He claimed that Lundy's perjury and the FBI's disavowal of CABL evidence warranted reversal of his conviction and a new trial. In response, the government argued that Berry's motion was barred by the one-year limitations period set out in 28 U.S.C. § 2255(f). On the merits, the government argued that Berry's motion should be treated as a motion for a new trial and that it should be denied because the new evidence was not "such that a new trial would probably produce an acquittal." See Jackson, 209 F.3d at 1106.
The district court found that Berry's § 2255 motion was timely and, treating it as a motion for a new trial, denied the motion on the merits. We issued a certificate of appealability to determine whether the new evidence warranted a new trial.

II. THE COGNIZABILITY OF BERRY'S CLAIMS
Before turning to the merits of Berry's appeal, we must first address the *1038 cognizability of Berry's claims. As noted above, Berry brought his motion under 28 U.S.C. § 2255. Congress enacted § 2255 to simplify the habeas process for federal prisoners. The section provides "a remedy [in the sentencing court] exactly commensurate with that which had previously been available by habeas corpus in the court of the district where the prisoner was confined." Hill v. United States, 368 U.S. 424, 427, 82 S.Ct. 468, 7 L.Ed.2d 417 (1962). Because a § 2255 motion is "commensurate" with habeas relief, it may only be used to collaterally attack a conviction and sentence "upon the ground that the sentence was imposed in violation of the Constitution or laws of the United States." 28 U.S.C. § 2255; see also United States v. Wilcox, 640 F.2d 970, 972 (9th Cir.1981) ("[Motions under § 2255 are limited to:] (1) constitutional issues, (2) challenges to the district court's jurisdiction to impose the sentence, (3) challenges to the length of a sentence imposed in excess of the statutory maximum, and (4) claims that the sentence is otherwise subject to collateral attack.").
The Supreme Court has repeatedly stressed the limits of a § 2255 motion. For example, the Court has cautioned that § 2255 may not be used as a chance at a second appeal. See, e.g., United States v. Addonizio, 442 U.S. 178, 184, 99 S.Ct. 2235, 60 L.Ed.2d 805 (1979) ("When Congress enacted § 2255 in 1948,. . . it did not purport to modify the basic distinction between direct review and collateral review."). Further, short of proof of actual innocence,[5] claims solely based on new evidence are generally not cognizable on habeas. See Conley v. United States, 323 F.3d 7, 14 (1st Cir.2003) (en banc) ("Merely to claim that new evidence casts doubt, even grave doubt, on the correctness of a conviction is not a ground for relief on collateral attack."). Rather, a motion under § 2255 must be based upon an independent constitutional violation. See Herrera v. Collins, 506 U.S. 390, 400, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993) ("[N]ewly discovered evidence . . . alleged in a habeas application . . . must bear upon the constitutionality of the applicant's detention; the existence merely of newly discovered evidence relevant to the guilt of a state prisoner is not a ground for relief on federal habeas corpus." (emphasis in original) (quoting Townsend v. Sain, 372 U.S. 293, 317, 83 S.Ct. 745, 9 L.Ed.2d 770 (1963))); Turner, 281 F.3d at 872 (rejecting habeas claim based upon newly discovered evidence because the petitioner "neither allege[d] an independent constitutional violation nor present[ed] affirmative proof of his innocence").
With one exception, Berry's § 2255 motion did not allege an independent constitutional violation. Instead, Berry claimed that Lundy's perjury conviction and the FBI's discontinuation of CABL evidence called into doubt the overall weight of the evidence against him. Such an evidence-based claim, however, is not cognizable under § 2255. The proper device for such a claim is Federal Rule of Criminal Procedure 33, which allows a prisoner to move for a new trial based on newly discovered evidence. Fed.R.Crim.P. 33(b)(1). Rule 33 also requires that a prisoner bring such a motion within three years of the date of his guilty verdict. Id.
*1039 Berry, proceeding pro se before the district court, did not appreciate the distinction between these motions. Thus, he filed his § 2255 motion ten years after his conviction, raising claims that were long-since barred by Rule 33's three-year period of limitations. Neither the district court nor the government noticed that Berry was attempting to revive evidencebased claims that had long since expired.
The confusion of the parties and the district court was doubtless aided by a sentence from our opinion in Jackson. There, we stated, without elaboration, that a motion under § 2255 that raises evidence-based claims should be treated as a motion for a new trial. 209 F.3d at 1106 ("We treat Jackson's motion under 28 U.S.C. § 2255 as a motion for a new trial."). What we did not explain, however, because there was no occasion to do so, was that the § 2255 motion in that case had been filed within the time period allowed for new trial motions, at that time two years from the date the mandate issued from this court.[6] Thus, we were free to treat the § 2255 motion as a motion for a new trial because such a motion would have been timely. That is not the case here; Berry filed his motion almost ten years after his original conviction and was therefore well out of time. See Fed. R.Crim.P. 33(b)(1) (imposing limitations period of three years from date of conviction for motion for a new trial based upon newly discovered evidence).
Given this confusion, we now take this opportunity to clarify our holding in Jackson. A district court may treat a § 2255 motion as a Rule 33 motion for a new trial. See Jackson, 209 F.3d at 1106. To do so, the § 2255 motion must be timely under the provisions of Rule 33. But the Rule 33 time limitation is not jurisdictional and is thus waivable if the government does not object to an untimely motion. Eberhart v. United States, 546 U.S. 12, 13, 126 S.Ct. 403, 163 L.Ed.2d 14 (2005) (per curiam). Accordingly, when a prisoner files a § 2255 motion that is untimely under Rule 33, the district court may still treat it as a Rule 33 motion if the government has waived any objection to Rule 33 timeliness. With this clarification, we now turn to the merits of Berry's claims.

III. THE MERITS OF BERRY'S CLAIMS
As noted above, Berry's § 2255 motion raised two claims. First, Berry asserted that the CABL evidence was so scientifically unsound that it rendered his trial "fundamentally unfair," in violation of his due process rights. Second, he argued that Lundy's perjury and the FBI's discontinued use of CABL evidence undermines confidence in his guilty verdict. We find neither argument convincing.

A. Berry's Due Process Claim

Berry's motion raised a single claim that is cognizable under § 2255: that the CABL evidence used at his trial was so arbitrary as to render his trial fundamentally unfair.[7]See Jackson v. Brown, 513 *1040 F.3d 1057, 1082 (9th Cir.2008) ("Even if the state court admitted the evidence in error, we cannot disturb the state trial court's admission of [evidence] on due process grounds in a habeas proceeding unless the admission . . . rendered the trial fundamentally unfair." (internal quotation marks omitted) (alteration in original)). We review the district court's denial of this claim de novo. United States v. Day, 285 F.3d 1167, 1169 (9th Cir.2002).
In order for Berry to succeed on his due process claim, it is not enough that the evidence introduced against him was of low probative value or was of questionable reliability. Rather, Berry must establish that the evidence was so arbitrary that "the factfinder and the adversary system [were] not . . . competent to uncover, recognize, and take due account of its shortcomings." Barefoot v. Estelle, 463 U.S. 880, 899, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983), superseded on other grounds by 28 U.S.C. § 2253(c)(2).
In Barefoot, for example, the Court rejected the argument that a psychologist could not testify as to a defendant's future dangerousness, despite the fact that the American Psychological Association had submitted an amicus brief against the practice. Id. at 896-902, 103 S.Ct. 3383. In reaching this conclusion, the Court noted that a psychologist's future-dangerousness prediction was not "almost entirely unreliable," id. at 899, 103 S.Ct. 3383, and emphasized the ability of the adversary process to determine the appropriate weight that a psychologist's testimony should receive, id. at 901, 103 S.Ct. 3383 ("We are unconvinced, however, at least as of now, that the adversary process cannot be trusted to sort out the reliable from the unreliable evidence and opinion about future dangerousness, particularly when the convicted felon has the opportunity to present his own side of the case.").
We have also rejected a collateral attack that was based on the introduction of evidence of questionable probative value. In Mancuso v. Olivarez, 292 F.3d 939 (9th Cir.2002), we rejected the petitioner's argument that his constitutional rights were violated by the introduction at trial of his post-hypnotic statements, despite our concerns about their reliability. Id. at 956. While we acknowledged the questionable nature of the evidence, we emphasized that it was sufficiently reliable to warrant recourse to the normal adversary process to expose any flaws in the science. Id.; see also Barefoot, 463 U.S. at 899, 103 S.Ct. 3383.
While the CABL evidence introduced against Berry may have been flawed, we do not find it so arbitrary as to render Berry's trial "fundamentally unfair." The criticisms of CABL evidence that Berry relies on indicate that it is precisely the kind of evidence that the adversary system is designed to test. Vigorous cross-examination would have exposed its flaws to the jury.
The National Research Council's criticisms certainly fit this description. For example, the National Research Council report cautioned that "[v]ariations among and within lead bullet manufacturers make any modeling of the general manufacturing process unreliable and potentially misleading in CABL comparisons." Nat'l Res. Council, supra, at 112. The report's most serious caution concerned the extent of the conclusions CABL analysis could support:

*1041 The available data do not support any statement that a crime bullet came from, or is likely to have come from, a particular box of ammunition, and references to "boxes" of ammunition in any form are seriously misleading under Federal Rule of Evidence 403.
Testimony that the crime bullet came from the defendant's box or from a box manufactured at the same time, is also objectionable because it may be understood as implying a substantial probability that the bullet came from defendant's box.
Id. at 113. Both of these criticisms could easily have been brought out on cross-examination.
Other studies have provided more significant critiques of CABL evidence, challenging some of the basic assumptions that underlie the forensic technique. They do not, however, establish that the science was "almost entirely unreliable." For example, some studies have taken issue with CABL's assumption that a block of lead is homogenous. See Clemons, 896 A.2d at 1076-77 (describing studies and concluding that "the assumption that an ingot or vat of lead is homogenous as required for [CABL] to be valid is not generally accepted by the scientific community"). If a block is not homogenous, then two bullets produced from the same melt might have different chemical profiles. Other studies have opined that "analytically indistinguishable" bullets could easily come from different blocks of lead, leading CABL to generate a false positive result. Id. at 1077-78.
These are undoubtedly significant criticisms of CABL evidence. Berry, however, has not explained why he was prevented from presenting such criticisms to the jury, either through vigorous cross-examination or by calling his own expert witness.
Thus, while the above studies may caution against widespread usage of CABL evidence, we do not believe they establish that CABL evidence is so fundamentally unreliable that its introduction at Berry's trial violated his due process rights. Indeed, the National Research Council concludes that CABL analysis is still reliable enough to be used at trial:
It is the conclusion of the committee that, in many cases, CABL is a reasonably accurate way of determining whether two bullets could have come from the same compositionally indistinguishable volume of lead. It may thus in appropriate cases provide additional evidence that ties a suspect to a crime, or in some cases evidence that tends to exonerate a suspect. CABL does not, however, have the unique specificity of techniques such as DNA typing to be used as standalone evidence.
Nat'l Res. Council, supra, at 109; see also id. at 112 ("CABL is sufficiently reliable to support testimony that bullets from the same compositionally indistinguishable volume of lead (CIVL) are more likely to be analytically indistinguishable than bullets from different CIVLs. An examiner may also testify that having CABL evidence that two bullets are analytically indistinguishable increases the probability that two bullets come from the same CIVL, versus no evidence of match status.").
In any event, even if CABL evidence were generally unreliable, we would still be inclined to reject Berry's due process challenge based upon the reliability of the specific testimony in his case. Lundy's testimony was not susceptible to any of the criticisms identified in the National Research Council report. In particular, Lundy did not testify that the CABL tests definitively linked Berry to the Planned Parenthood pipe bomb. In fact, she repeatedly stated that she could not determine whether the buckshot from the bomb came from the bags found in Berry's shop. *1042 Instead, she testified only that the buckshot from the two sources had identical chemical profiles.
Lundy's analysis was also highly individualized to the unique factual circumstances of Berry's case. She investigated the precise manner in which Hornaday lead was manufactured and adjusted her conclusions based upon that firm's manufacturing processes. Cf. Nat'l Res. Council, supra, at 112 (cautioning against use of generalization in bullet manufacturing process). Further, the fact that the pipe bomb contained buckshot allowed Lundy to test multiple samples and to compare their chemical consistency; Lundy testified that she tested 26 pellets from the pipe bomb and 15 from Berry's autoshop. Finally, Lundy's determination that the pipe bomb buckshot was 3 percent antimonya feature unique to Hornaday buckshotlinked Berry to the pipe bomb regardless of the CABL tests.
The reliability of Lundy's testimony was also buttressed by Hanson, who confirmed Lundy's major conclusions. Hanson, for example, testified that Hornaday was to his knowledge the only manufacturer that used lead with 3 percent antimony. And it was Hanson's testimony that Hornaday shipped only thirty-two bags of buckshot to the Spokane area that provided the strongest connection between Berry and the Planned Parenthood pipe bomb.
Thus, the CABL evidence used against Berry does not appear to suffer from the flaws to which the science may otherwise be susceptible. Simply put, given the circumstances of this case, Lundy's conclusions were not overstated and appear to be quite reliable.
Based on the above, the criticisms of Lundy's CABL analysis concern the proper weight of the evidence, not its admissibility. It can hardly be said, therefore, that the adversary system was not "competent to uncover, recognize, and take due account of its shortcomings." Barefoot, 463 U.S. at 899, 103 S.Ct. 3383. Accordingly, we reject Berry's due process claim.

B. Berry's New Trial Claim

The remainder of Berry's § 2255 motion concerns the effect that the new evidence would have had on his trial, and therefore falls into the realm occupied by new trial motions under Rule 33. Ordinarily, we would find Berry's new-trial claims well out-of-time, because he filed his § 2255 motion almost seven years after a Rule 33 motion was due. Given that Berry proceeded pro se before the district court, however, and that the government did not specifically object to Berry's new-trial claims below, we hold that the government waived its objection to the timeliness of those claims. See Eberhart, 546 U.S. at 13, 126 S.Ct. 403 (finding's Rule 33's time limits to be waivable and not jurisdictional).
We therefore treat the district court's denial of Berry's § 2255 motion as the denial of a motion for a new trial, which we review for abuse of discretion. United States v. Mack, 362 F.3d 597, 600 (9th Cir.2004). We conclude that the district court did not abuse its discretion in finding the new evidence Berry produced insufficient to warrant a new trial.
To qualify for a new trial, Berry must establish: "(1) the evidence is newly discovered; (2) the defendant was diligent in seeking the evidence; (3) the evidence is material to the issues at trial; (4) the evidence is not (a) cumulative or (b) merely impeaching; and (5) the evidence indicates the defendant would probably be acquitted in a new trial." United States v. Hinkson, 585 F.3d 1247, 1264 (9th Cir. 2009) (en banc). The district court denied Berry's motion on the ground that the new evidence was both "merely impeaching" and unlikely to result in an acquittal on retrial. We agree.
*1043 For the reasons discussed above, we conclude that the National Research Council report and the FBI's discontinued use of CABL evidence were no more than impeaching evidence of the CABL testimony introduced at Berry's trial. We also reject Berry's contention that the evidence of Lundy's false statement was more than "merely impeaching." The false statement occurred almost five years after Berry's trial and related to a bullet-manufacturing process that was not at issue in his case. Further, Lundy was not accused of fabricating the results of any tests in this case, and there is no evidence that she committed perjury at Berry's trial. Thus, there is little doubt that the new evidence would only serve to impeach her credibility on retrial.
Berry relies on three casesMesarosh v. United States, 352 U.S. 1, 77 S.Ct. 1, 1 L.Ed.2d 1 (1956), Williams v. United States, 500 F.2d 105 (9th Cir.1974), and United States v. Chisum, 436 F.2d 645 (9th Cir. 1971)for his argument that he deserves a new trial. We have limited application of those cases, however, to those "rare" situations "where the credibility of a key government witness has been `wholly discredited' by the witness' commission of perjury in other cases involving substantially similar subject matter." See United States v. Krasny, 607 F.2d 840, 845 (9th Cir.1979); see also United States v. Stofsky, 527 F.2d 237, 246 (2d Cir.1975) ("[T]his court has noted that Mesarosh is a sui generis case, involving that rare situation where a key witness ... had been conceded by the government to have testified... in such a bizarre fashion as to raise the inference that he was either an inveterate perjurer or a disordered mind." (internal citations and quotation marks omitted)). Lundy's false statement, limited to one date at one trial, is a far cry from this high standard.
Finally, the new evidence would not "probably" result in an acquittal if a new trial were granted. As outlined above, significant circumstantial evidence connected the defendants to the robberies and bombings. In fact, even without the CABL evidence, there was sufficient evidence to support Berry's conviction. The district court did not abuse its discretion by finding that Berry's new evidence would not have made any difference in the outcome of his trial.

IV. CONCLUSION
For the foregoing reasons, we reject Berry's constitutional challenge to his conviction and his request for a new trial. The district court's denial of his § 2255 motion is therefore
AFFIRMED.
NOTES
[1]  According to testimony at Berry's trial, the Phineas Priesthood is not an organization per se, but is a term used by individuals who are committed to an extreme view of "God's Law." Those who self-identify as members of the Phineas Priesthood advocate the separation of people of different races and religions and believe in a ban on usury. The symbol of the Phineas Priesthood consists of a capital "P" merged with a cross.
[2]  At a separate trial, a fourth man was also convicted of participating in the Planned Parenthood bombing and the July 12 bank robbery. His conviction was upheld on appeal along with the convictions of Berry, Barbee, and Merrell. See United States v. Merrell, 182 F.3d 929 (table), 1999 WL 386651 (9th Cir. 1999).
[3]  Bullets are created by placing large, cylindrical blocks of lead known as billets into an extrusion press, forcing the lead into a thin wire that is later cut into individual bullets. A bullet manufacturer can either purchase lead from a supplier in billet form, or it can purchase blocks of lead that it remelts into billets at its manufacturing plant. A key assumption of CABL is that melting lead causes the impurities in the lead to become distributed evenly throughout the batch, making all bullets produced from that melt chemically identical. CABL also assumes that each batch of melted lead will have a unique combination of impurities, which can be used as a sort of chemical fingerprint to identify bullets made from that particular batch.
[4]  Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993).
[5]  This circuit recognizes a claim of actual innocence that is cognizable under § 2255. See Carriger v. Stewart, 132 F.3d 463, 476 (9th Cir.1997) (en banc) (holding that a prisoner's freestanding innocence claim must "affirmatively prove that he is probably innocent"); see also Turner v. Calderon, 281 F.3d 851, 872-73 (9th Cir.2002). Berry does not argue that his new evidence meets this standard.
[6]  Under the version of Rule 33 that existed at the time of Jackson's § 2255 motion, Jackson had two years from the date the mandate issued from this court to file his motion for a new trial. See United States v. Cook, 705 F.2d 350, 351 (9th Cir.1983) (finding that, for purposes of former Rule 33, "final judgment" was the date on which the "appellate court issues its mandate of affirmance"). Jackson's direct appeal was dismissed on July 25, 1995, and the mandate issued on December 26, 1995. Thus, Jackson's § 2255 motion, filed on April 22, 1997, was filed well before the deadline for new-trial motions established by former Rule 33.
[7]  In addition to the above argument, Berry claims on appeal that the government committed a Brady violation when it failed to disclose that Berry's brother, Loren Berry, was compensated for the testimony he gave at Berry's trial. Berry raised this claim for the first time in his reply brief before the district court; he did not identify the claim in either his motion or in his initial supporting memorandum. Because the Brady claim was not included in his § 2255 motion, it was not addressed by the district court and falls outside the scope of our certificate of appealability.
