Krasny appeals from a district court judgment denying his motion for a new trial. He based his motion upon newly discovered evidence which purportedly demonstrates that a government witness committed perjury during his trial. Krasny argues that the district court applied an incorrect legal standard and failed to make necessary findings in ruling on his motion for a new trial. We conclude that the district judge did not apply a test that requires us to reverse. However, because his findings are insufficient to allow us to determine whether he abused his discretion, we vacate the judgment denying Krasny’s motion and remand for further proceedings.
I
We earlier affirmed Krasny’s conviction on charges of conspiracy to import heroin into the United States, and to possess heroin with intent to distribute, in violation of 21 U.S.C. §§ 841(a)(1), 846, 952, 963. His conviction arose out of an alleged agreement between him and two others, Bennett and Worley, to import heroin from Bangkok into the United States. Bennett first trav*842eled to Bangkok to obtain the heroin. Worley followed Bennett, secured the heroin, and was arrested when she attempted to smuggle it into the United States.
After her arrest, Worley cooperated with the government and consented to the taping of conversations between her and Krasny. The government’s case against Krasny rested on these conversations and the testimony of Worley. She testified that Krasny was a principal in the conspiracy, while she merely acted as his agent, traveling to Bangkok at his behest. Worley also claimed that before the trip she had never discussed the subject of narcotics with Bennett. She admitted traveling to Mexico on two occasions with Bennett, who told her that the trips were for the purpose of acquiring narcotics. However, she denied taking part in any of these narcotics transactions, and testified that only Bennett had been involved, while she just went as his companion.
The taped conversations revealed, among other things, that Krasny had been at the airport in Honolulu to meet Worley upon her return from Bangkok, that his sole purpose in going to Honolulu may well have been to meet her, that he later planned to send someone else to meet her in Honolulu, that he had been a “nervous wreck” because Worley did not leave customs when he expected her to, that he was familiar with the customs area in Honolulu, that he had people who were “dying” to get the “stuff,” and that he could pay Worley in two days, after he sold it.
Krasny’s version of the events and his explanation of the phone calls differed from those of Worley. He testified that he had never before had anything to do with Worley’s and Bennett’s dealings in heroin. Krasny did not deny participation in the taped phone calls. He claimed, however, that he had been coerced by threats against him and his family into agreeing to assist Worley in the delivery of the heroin. The jury obviously did not believe this defense, as it convicted Krasny for his involvement in the conspiracy.
Subsequent to Krasny’s conviction, the government, with commendable candor, advised his attorney of new developments concerning Worley’s trial testimony. The government discovered that Worley had, in fact, assisted Bennett to some degree in prior narcotics transactions, despite her earlier testimony to the contrary. Specifically, Worley admitted that she had mailed some packages containing cocaine on Bennett’s behalf. She also stated that she had participated in a number of conversations with Bennett regarding narcotics, some in the presence of Krasny.
Worley first explained that she failed to admit, during cross-examination, her prior narcotics involvement with Bennett because it was none of Krasny’s counsel’s business. Subsequently, however, she apparently indicated that she did not really mean that that was the reason for her initial denial of this involvement, but the record does not reveal any other reason for her apparently erroneous testimony. In any event, the parties agree that neither the government nor Krasny knew or had reason to know of Worley’s more extended involvement with Bennett in narcotics trafficking.
The district judge did not rule specifically whether he believed that Worley had perjured herself. In denying Krasny’s motion for a new trial, however, he did rule that “the suggested new evidence is at best cumulative and would not be of sufficient import to alter the jury’s determination in this matter in terms of guilt or innocence.”
II
Krasny’s challenge to the judge’s ruling on his motion raises a question of apparent first impression in this circuit. We must decide the correct standard for granting a new trial when newly discovered evidence reveals that a government witness may have committed perjury during the trial.1
In general, a defendant seeking a new trial on the basis of newly discovered evidence must meet the following requirements:
*843“(1) It must appear from the motion that the evidence relied on is, in fact, newly discovered, i. e., discovered after the trial; (2) the motion must allege facts from which the court may infer diligence on the part of the movant; (3) the evidence relied on must not be merely cumulative or impeaching; (4) must be material to the issues involved; and (5) must be such as, on a new trial, would probably produce an acquittal.”
United States v. Cervantes, 542 F.2d 773, 779 (9th Cir. 1976) (emphasis supplied) (quoting Pitts v. United States, 263 F.2d 808, 810 (9th Cir.), cert. denied, 360 U.S. 919, 79 S.Ct. 1438, 3 L.Ed.2d 1535 (1959)); accord, e. g., United States v. Brashier, 548 F.2d 1315, 1327 (9th Cir. 1976), cert. denied, 429 U.S. 1111, 97 S.Ct. 1149, 51 L.Ed.2d 565 (1977); United States v. Craft, 421 F.2d 693, 695 (9th Cir. 1970). A majority of circuits that have considered the question, however, have applied, or implied that they would apply, a modified standard when the newly discovered evidence indicates that a government witness committed perjury at trial. Rather than requiring a defendant to. show that an acquittal probably would result, these courts require only that the defendant demonstrate that an acquittal might or possibly would result upon a new trial. See, e. g., United States v. Wallace, 528 F.2d 863, 866 (4th Cir. 1976) (witness recantation); United States v. Anderson, 165 U.S.App.D.C. 390, 405, 509 F.2d 312, 327 n.105 (D.C.Cir.1974) (dictum), cert. denied, 420 U.S. 991, 95 S.Ct. 1427, 43 L.Ed.2d 672 (1975); United States v. Smith, 433 F.2d 149, 151 (5th Cir. 1970) (per curiam); Gordon v. United States, 178 F.2d 896, 900 (6th Cir. 1949), cert. denied, 339 U.S. 935, 70 S.Ct. 664, 94 L.Ed. 1353 (1950); Larrison v. United States, 24 F.2d 82, 87 (7th Cir. 1928). See generally 2 C. Wright, Federal Practice and Procedure § 557, at n.24 (1969 & Supp. 1979). The “possibility” standard is often referred to as the “Larrison rule” because of its apparent origin in Larrison v. United States, supra.2
At times, courts have not completely endorsed this rule. Thus, courts may cite the Larrison rule with tacit approval, but decide that the defendant has failed to demonstrate the necessity of a new trial as judged by either standard, United States v. Hamilton, 559 F.2d 1370, 1372-73, 1374 & n.8 (5th Cir. 1977), or that the evidence merits a new trial pursuant to either rule, United States v. Meyers, 484 F.2d 113, 117 (3d Cir. 1973).
Recently, the Second Circuit severely criticized the Larrison standard, observing:
[T]he test, if literally applied, should require reversal in cases of perjury with respect to even minor matters, especially in light of the standard jury instruction that upon finding that a witness had deliberately proffered false testimony in part, the jury may disregard his entire testimony. Thus, once it is shown that a material witness has intentionally lied with respect to any matter, it is difficult to deny that the jury, had it known of the lie, “might” have acquitted.
*844United States v. Stofsky, 527 F.2d 237, 245-46 (2d Cir. 1975), cert. denied, 429 U.S. 819, 97 S.Ct. 65, 50 L.Ed.2d 80 (1976). Stofsky further stated that courts following the Larrison approach were not troubled by its “speculative nature,” and in many cases “have not hesitated to deny new trials in cases where they have purported to apply it.” Id. at 246 (footnote omitted). The court concluded:
[R]ather than adopt the Larrison test and violate it in application, we believe, for the reasons indicated, that the time-honored “probability” standard is the more appropriate one for determining whether perjury calls for a new trial. In addition to its other virtues the rule enables a court to act forthrightly in making its determination.
Id.
We are of the opinion that the court in Stofsky has taken the correct path, and we agree with its reasoning. We are unpersuaded, on the other hand, by the reasoning used in justification of the Larrison rule. For example, the court in Larrison relied only upon Martin v. United States, 17 F.2d 973 (5th Cir.), cert. denied, 275 U.S. 527, 48 S.Ct. 20, 72 L.Ed. 408 (1927), which held that the cumulative nature of perjured testimony alone should not be determinative of whether a new trial is to be granted. 24 F.2d at 87. That court reasoned:
There is no way for a court to determine that the perjured testimony did not have controlling weight with the jury, and, notwithstanding the perjured testimony was contradicted at the trial, a new light is thrown on it by the admission that it was false; so that, on a new trial, there would be a strong circumstance in favor of the losing party that did not exist, and therefore could not have been shown, at the time of the original trial.
17 F.2d at 976. We do not entirely disagree with this statement. Of course, there is no sure method of determining the weight of the perjured testimony. But there is similarly no certainty in evaluating the weight which any newly discovered evidence would have on a jury’s deliberations. Yet when such grounds are presented, this is precisely the determination that courts generally make.
The court in United States v. Johnson, 149 F.2d 31, 44 (7th Cir. 1945), rev’d on other grounds, 327 U.S. 106, 66 S.Ct. 464, 90 L.Ed. 562 (1946), developed a different argument in favor of the Larrison rule. Without explaining the difference, the court suggested that, while most motions for a new trial concern the probable effect of newly discovered evidence on a future trial, motions for a new trial based upon the perjury of a government witness concern the probable effect of the perjured testimony on the first trial. We cannot see any practical difference in this distinction. Johnson also quoted Pettine v. Territory of New Mexico, 201 F. 489, 494 (8th Cir. 1912): “ ‘Is it clear beyond doubt that this testimony did not turn the scales against him or remove from the mind of some juror a reasonable doubt of his guilt?’ ” United States v. Johnson, supra, 149 F.2d at 44. While this query may, at first blush, appear superficially to be a valid test, the case does not suggest any effective difference between perjured testimony and other new evidence, and we can conceive of none. The focus of the inquiry is on what difference the evidence would have made to the trial, regardless of its source.
One may always ask how courts can be certain that new evidence would not create a reasonable doubt in the mind of at least one juror. Yet, we have always required a showing that the new evidence would “probably” result in an acquittal upon a new trial. We are not convinced that all cases involving some perjured testimony necessarily require new trials. Yet, as the court in United States v. Stofsky, supra, 527 F.2d at 246, observed, this is exactly where the logic of such cases as Larrison, Martin, and Pettine leads.
We are thus in agreement with Stofsky that the probability standard is appropriate for determining whether perjury requires a new trial, 527 F.2d at 246, at least when the government did not knowingly or negligently use the perjured testi*845mony, see id. at 245. When a key witness recants his or her testimony in its entirety, or the bulk of a key witness’ testimony is otherwise shown to be false, a district court may well find it probable that an acquittal would result on retrial, and may not so find when a rather inconsequential witness has prevaricated on a minor or collateral issue.3 A per se rule is not required.
Ill
Krasny suggests that this view is in conflict with the teachings of the Supreme Court in Mesarosh v. United States, 352 U.S. 1, 77 S.Ct. 1, 1 L.Ed.2d 1 (1956). There, the Court had before it, on direct review, the convictions of a number of defendants for conspiracy to violate the Smith Act. The Solicitor General revealed that a key government witness had apparently testified untruthfully in the same role in other similar proceedings. The Supreme Court, making clear that it was not ruling on a motion for a new trial pursuant to Rule 33 of the Federal Rules of Criminal Procedure, stated that the witness’ “credibility [had] been wholly discredited,” id. at 9, 77 S.Ct. 1, and that it would be “unreasonable” to find that “the witness . testified truthfully in this case in 1953 as an undercover informer concerning the activities of the Communist conspiracy, yet concurrently appeared in the same role in another tribunal and testified falsely . about a plan by different members of the Communist conspiracy to assassinate a United States Senator,” id. at 13, 77 S.Ct. at 7 (footnote omitted). This being so, a majority of the Court believed that a new trial was required. Cf. Communist Party of the United States v. Subversive Activities Control Bd., 351 U.S. 115, 124, 76 S.Ct. 663, 668, 100 L.Ed. 1003 (1956) (“If these witnesses in fact committed perjury in testifying in other cases on subject matter substantially like that of their testimony in the present proceedings, their testimony in this proceeding is inevitably discredited . . . .”).
We have followed this approach in cases where the factual circumstances have closely paralleled those found in Mesarosh. See Williams v. United States, 500 F.2d 105 (9th Cir. 1974); United States v. Chisum, 436 F.2d 645 (9th Cir. 1971). We believe that the principles which guided the Court in Mesarosh are limited in application to those rare cases 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. Stofsky, supra, 527 F.2d at 246.
IV
We thus conclude that Krasny cannot complain about the test applied by the district judge. In finding that the “new evidence . . . would not alter the jury’s determination,” the judge a fortiori found that it would not “probably” do so.4
The decision, when based upon the proper legal standard, to grant or deny a motion for a new trial based upon newly discovered evidence is within the sound discretion of the trial judge. United States v. Craft, supra, 421 F.2d at 695; see, e. g., *846United States v. Cervantes, supra, 542 F.2d at 779; Pitts v. United States, supra, 263 F.2d at 811. Krasny carries a “significant” burden to show that the district judge abused his discretion. United States v. Brashier, supra, 548 F.2d at 1327. While Krasny argues that the district judge did so here,5 he also claims that the judge’s failure to make a specific factual finding as to whether Worley committed perjury requires us at least to remand the case for this determination.
We are left in such doubt that we are constrained to agree that the case must be remanded. The record is insufficient for us to test fairly the determination made by the district court. Nor do we fault the district judge for this deficit. The law of our circuit was unclear as to what test he was to apply. In fairness and because he is in the best position to decide the issue, we believe the district judge should now be given the first opportunity to apply the test.6
We concur in the Second Circuit’s view regarding the proper analysis of motions for a new trial which are based upon allegations that a government witness committed perjury at trial.
Upon discovery of previous trial perjury by a government witness, the court should decide whether the jury probably would have altered its verdict if it had had the opportunity to appraise the impact of the newly-discovered evidence not only upon the factual elements of the government’s case but also upon the credibility of the government’s witness.
United States v. Stofsky, supra, 527 F.2d at 246. As Stofsky persuasively argued, the witness’ credibility could very well have been as important to the jury as the factual elements of the perjured testimony. See id.
On remand, if the district judge determines that Worley appeared to have committed perjury, he will need to consider, among other things, the importance of Worley’s testimony to the government’s case, the extent to which the apparently perjured testimony concerned material issues in the case, and the extent to which her credibility, as a whole, would be affected by the revelation to the jury of this apparent perjury. Based upon this analysis, the district judge will be able to make a finding as to whether Krasny has proved that had newly discovered evidence been presented during the trial, the jury probably would have acquitted him.
Because we cannot properly evaluate the district court’s exercise of discretion, we vacate and remand the case so that the district judge can make the necessary findings.
VACATED AND REMANDED.
. We have never before fully analyzed this' question. See footnote 2.
. We have cited this case just once, and then only as authority for the “probable” standard. See United States v. Sloan, 465 F.2d 406, 407 (9th Cir. 1972) (per curiam).
While we have employed “might” language in two cases, neither of these is dispositive of the issue before us. In Mejia v. United States, 291 F.2d 198 (9th Cir. 1961), the appellant had made an admission of guilt which he had unsuccessfully attempted to explain away at trial. When the appellant subsequently produced an alibi witness, we ordered a new trial, observing that “the jury might in view of [the alibi witness’] testimony, accept the appellant’s story that he was a mere braggart, and not telling the truth when he asserted” that he had engaged in criminal activity. Id. at 201. We made it very clear, however, that we decided that case only “upon the special and peculiar facts” before us there. Id. at 201 n.3. No such “special and peculiar facts” are present here.
In Strangway v. United States, 312 F.2d 283, 286 (9th Cir.), cert. denied, 373 U.S. 903, 83 S.Ct. 1291, 10 L.Ed.2d 199 (1963), we stated: “Appellant also invokes the rule that a conviction cannot stand where the testimony of a material witness is false and without which a jury might have reached a different conclusion . .” We explained, however, that the case before us there did not involve any “newly-discovered evidence [tending] to show that a major witness for the prosecution had testified falsely at . trial,” id. Therefore, there was no reason to adopt or reject the rule in that case. We now squarely face the question.
. We find support for this view in Professor Moore’s reasoning that two of the traditional prerequisites for prevailing on a motion for a new trial based upon newly discovered evidence, i. e., that the newly discovered evidence be material and that it probably would produce an acquittal on retrial, are really two means of measuring the same thing. 8A J. Moore, Moore’s Federal Practice ¶ 33.04[1], at 33-27 (2d ed. 1978). Professor Moore harmonizes the Larrison rule with this view, observing: “Since the ultimate question is whether the new evidence ‘could have induced a reasonable doubt in the minds of enough jurors to avoid a conviction,’ it follows that the testimony of a principal government witness inherently possesses a high degree of materiality.” Id. (footnotes omitted).
While it may be that “the testimony of a principal government witness inherently possesses a high degree of materiality,” we do not agree that this fact calls for a different test. Rather, it is a factor naturally to be taken into account in applying the usual test.
. Moreover, a fair reading of the transcript of the hearing on the motion for a new trial makes clear that the district judge had in mind the “probable” standard.
. Krasny suggests that a new trial is required because if the jury believed Worley’s allegedly perjured denial that she had a principal role in the narcotics transactions, as well as her testimony that painted such a role for Krasny, then the jury could not possibly have believed Krasny’s duress defense. The government, in response, argues that the newly discovered evidence merely expands on Bennett’s role in narcotics trafficking “although also showing a greater but still limited role for Worley. It does not contradict any testimony Worley gave concerning Krasny’s activities.” The government concludes that the district judge correctly viewed the newly discovered evidence as “merely cumulative.” In view of our remand, we need not now resolve this conflict.
. Thus, we do not follow the ultimate disposition made in Stofsky, in which the Second Circuit concluded that it could not “say that disclosure of [the witness’] perjury ‘probably’ would have produced a different verdict.” 527 F.2d at 247.