
    UNITED STATES of America, Appellee, v. Mark E. HUDDLESTON, Defendant, Appellant.
    No. 99-1144.
    United States Court of Appeals, First Circuit.
    Heard Aug. 4, 1999.
    Decided Oct. 19, 1999.
    
      Bruce M. Merrill, with whom Bruce M. Merrill, P.A. was on brief, for appellant.
    F. Mark Terison, Assistant United States Attorney, with whom Jay P. McCloskey, United States Attorney, was on brief, for appellee.
    Before SELYA, Circuit Judge, CYR, Senior Circuit Judge, and BOUDIN, Circuit Judge.
   SELYA, Circuit Judge.

For many years, the courts of appeals have been divided over what legal standard obtains when a convicted defendant premises a motion for new trial on a claim that he has newly discovered that the case against him was based in part on the prosecutor’s unwitting use of perjured testimony. Some courts apply a “probability” standard in such situations, granting relief only if the discovery “probably” or “likely” — courts in this context use the terms interchangeably, and we shall use the former — would lead to an acquittal. See United States v. Torres, 128 F.3d 38, 49 (2d Cir.1997), cert. denied, — U.S. -, 118 S.Ct. 1399, 140 L.Ed.2d 657 (1998); United States v. Sinclair, 109 F.3d 1527, 1532 (10th Cir.1997); United States v. Tierney, 947 F.2d 854, 860-61 (8th Cir.1991); United States v. Krasny, 607 F.2d 840, 844-45 (9th Cir.1979); United States v. Stofsky, 527 F.2d 237, 245-46 (2d Cir.1975). Others apply a “possibility” standard, granting relief whenever the discovery “might” have produced an acquittal. See United States v. Wallace, 528 F.2d 863, 866 (4th Cir.1976); Gordon v. United States, 178 F.2d 896, 900 (6th Cir.1949); Larrison v. United States, 24 F.2d 82, 87 (7th Cir.1928). The case at hand requires us to enter this debate and articulate our position.

We conclude that newly discovered evidence that the case against a defendant rested in part on a prosecutor’s unwitting use of perjurious testimony should be treated in the same manner as any other newly discovered evidence for purposes of post-conviction relief. Specifically, a court should grant a motion for a new trial based on the prosecutor’s unwitting use of perjured testimony only if the discovery of both the fact and nature of the perjured testimony, along with the content of the corrected testimony, probably would result in acquittal upon retrial. Thus, we reject the “possibility” standard in favor of the “probability” standard. Because the court below did not err in this or any other material respect, we affirm the judgment.

I. BACKGROUND

We sketch the facts, referring the reader who hungers for greater specificity to the district court’s more exegetic account. See United States v. Huddleston, 23 F.Supp.2d 72, 73-75 (D.Me.1998).

In June 1997, two members of a drug-distribution ring (Roberto Santana-Rivera, a/k/a “Chago,” and Miqueas Rodriguezs Gonzalez;, a/k/a “Gonzo”) began to cooperate with the federal- Drug Enforcement Administration (DEA). In the course of that endeavor, the DEA monitored a series of telephone calls in which Gonzo and defendant-appellant Mark E. Huddleston planned a cocaine buy. Tapes of these conversations memorialized such statements by the appellant as:

—Well, they got some customers lined up if you want to deliver.... I can go through an ounce anyway.
—You bring me an ounce and I’ll have your money within f_g five hours.

These conversations culminated in an agreement to meet at a Burger King restaurant in Kennebunk, Maine.

When the appellant kept the date, he was arrested and advised of his rights. He failed to heed the advice. At the scene, he was heard to say:

—[H]ey man, you got to eat. I’m tired of getting ripped off by dope dealers [down in Lowell]. You got to do what you got to do.
—[I]t’s only been since last fall, those guys made it easy for me. You guys are doing the right thing, you had to come and stop it some time.
—$650, two or three ounces, it’s not a lot, you know that.
—[TJhere’s three guys I deal to, that’s all, man.

En route to a nearby jail, the appellant remained loquacious. He told a DEA agent that he had started using and selling cocaine received from Chago and/or Gonzo as far back as March of 1997.

At trial, the government called Chago and Gonzo, among other witnesses. They identified themselves as Roberto Santana-Rivera and Miqueas Rodriguez-Gonzales, respectively, and each testified that the nature of his relationship with the appellant was as a cocaine source. On cross-examination, both men professed to be Puerto Rican rather than Dominican.

The appellant testified to his own be-hoof. He proclaimed an interest in exports to the Dominican Republic and linked his involvement with Chago and Gonzo to that embryonic enterprise. As part and parcel of this story, he claimed that Chago and Gonzo held themselves out to be Dominicans with extensive contacts in their homeland, and that, at Chago’s urging, he had restored several cars for export to that country. He denied that he planned to meet Gonzo at the Burger King on the day he was arrested for anything more sinister than to retrieve some personal belongings. In this vein, he explained that he requested “an ounce” from Gonzo because he hoped to lure Gonzo to his home so that he could ascertain where Gonzo lived and ultimately retrieve his belongings. When Gonzo declined, the appellant agreed to the Burger King rendezvous in a continuing effort to recover his possessions.

The jury rejected the appellant’s defense and found him guilty of both attempted possession of cocaine with intent to distribute and conspiracy to distribute. See 21 U.S.C. §§ 841(a), 846. At that point, the plot thickened: the government learned prior to sentencing that Chago and Gonzo had assumed false identities and nationalities, and that both men had lied on the witness stand anent these matters. In reality, the men were Dominican nationals (named Roland Garcia-Rodriguez and Pedro Herrara-Sarita, respectively), who had entered the country illegally. See United States v. Herrara-Sarita, 181 F.3d 81 (table), 1999 WL 525924, at *1, *3 (1st Cir.1999) (unpublished opinion encompassing sentencing appeals brought by Chago and Gonzo). The government promptly notified the appellant of its discovery.

Claiming that the government had failed to provide him with evidence material to his defense and that Chago’s and Gonzo’s perjury had tainted the verdict, the appellant moved for a new trial. See Fed. R.Crim.P. 33 (providing that the trial court “[o]n a defendant’s motion, ... may grant a new trial to that defendant if the interests of justice so require”). The district court denied the motion, see Huddleston, 23 F.Supp.2d at 79, and thereafter imposed a 24-month incarcerative sentence. This appeal ensued.

II. ANALYSIS

The appellant advances three propositions. His flagship argument involves a contention that the lower court misapprehended the legal standard to be applied to newly discovered evidence of perjury and that the correct standard, properly applied, mandates that his conviction be set aside. Next, he asseverates that the government’s failure to fulfill its pretrial disclosure obligations entitles him to another day in court. Finally, he contests the court’s calculation of the guideline sentencing range. We treat these arguments sequentially.

A. Perjured Testimony.

The appellant’s most cogent claim is that the government’s use of perjured testimony mandated a new trial. We review de novo the contention that the district court applied an incorrect legal standard. See In re Cusumano, 162 F.3d 708, 713 (1st Cir.1998) (holding that “ample authority supports the proposition that, whatever the procedural context, pure questions of law warrant de novo review”). Once past this barrier, however, the trial court’s application of the correct legal standard to the facts of a given case for the purpose of deciding a motion for a new trial is reviewed for abuse of discretion. See United States v. Natanel, 938 F.2d 302, 313 (1st Cir.1991).

As a general rule, four requirements must be satisfied before a court may grant a new trial on the ground of newly discovered evidence: (a) the evidence must have been unknown or unavailable to the defendant at the time of trial; (b) the defendant must have been duly diligent in attempting to unearth it; (c) the newly discovered evidence must be material; and (d) it must be such that its emergence probably will result in an acquittal upon retrial. See United States v. Tibolt, 72 F.3d 965, 971 (1st Cir.1995); United States v. Slade, 980 F.2d 27, 29 (1st Cir.1992); Natanel, 938 F.2d at 313.

The appellant contends, however, that a special, more defendant-friendly rule obtains in cases where, as here, the newly discovered evidence comprises perjured testimony: in such purlieus, he opines, a defendant need only show that the newly discovered evidence “might” produce a different result, not that it “probably” would produce a different result. This formulation, familiarly known as the Larrison rule, has been adopted in three circuits. See Wallace, 528 F.2d at 866 (4th Cir.); Gordon, 178 F.2d at 900 (6th Cir.); Larrison, 24 F.2d at 87 (7th Cir.). Four other circuits, however, have rejected it, at least insofar as it applies to the government’s unwitting use of perjured testimony. See Sinclair, 109 F.3d at 1532 (10th Cir.); Tierney, 947 F.2d at 860-61 (8th Cir.); Krasny, 607 F.2d at 844-45 (9th Cir.); Stofsky, 527 F.2d at 245-46 (2d Cir.).

The district court gave the appellant’s argument serious consideration, noting, inter alia, that if Larrison controlled, it would grant a new trial. See Huddleston, 23 F.Supp.2d at 78. But after a thoughtful exposition of the divided authorities, the court rejected the Larrison rule and found the appellant’s proffer wanting under either the standard for knowing prosecutorial presentation of perjured testimony, see Kyles v. Whitley, 514 U.S. 419, 433 n. 7, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995), or the traditional standard for newly discovered evidence. See Huddleston, 23 F.Supp.2d at 78-79. Although we frequently have mentioned the Larrison rule, we have not yet squarely addressed its validity. We do so today, concluding that the district court’s repudiation of the Lar-rison rule was correct.

The Seventh Circuit adopted the possibility standard without any developed reasoning. The Larrison court cited only Martin v. United States, 17 F.2d 973 (5th Cir.1927), and we assume that it found persuasive Martin’s suggestion that

[t]here 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.

Id. at 976. Whatever its inspiration, Lar-rison has drawn intense fire in its birthplace, see United States v. Mazzanti, 925 F.2d 1026, 1029 & nn. 2-3 (7th Cir.1991), and a number of courts have refused to follow it. These courts require a defendant who moves for a new trial based on newly discovered evidence, whether or not that evidence includes a showing that the government unwittingly used perjured testimony, to demonstrate that the newfound evidence (including evidence of the fact of perjury itself) probably would result in an acquittal upon retrial. We join these courts.

A principal difficulty with the Larrison rule is that it sweeps too broadly. It would be an unusual case in which newly discovered evidence of false testimony “might” not pave the way for an acquittal. In practice, therefore, Larrison comes perilously close to creating a per se rule that mandates a new trial whenever the government unwittingly uses perjured testimony. See Krasny, 607 F.2d at 843-44 (warning that Larrison, read literally, requires reversal even with respect to relatively minor instances of perjury); Stofsky, 527 F.2d at 245-46 (similar). While there may be no infallible way to gauge the effect of such an event on a jury, the same is true with regard to many other kinds of newly discovered evidence. Even if the testimony of a principal government witness is highly material, a court should import the revelation that the witness prevaricated into its normal decisional calculus rather than indulge in a false taxonomy. In short, we fail to see any substantial justification for treating the discovery of perjury differently than other newly discovered evidence.

Perhaps more important, we are persuaded that the Supreme Court, which deferred explicit decision of this question more than a half-century ago, see United States v. Johnson, 327 U.S. 106, 111 n. 4, 66 S.Ct. 464, 90 L.Ed. 562 (1946), would adopt the probability standard. In this respect, we find instructive the Court’s rationale in United States v. Agurs, 427 U.S. 97, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976). In the context of an alleged Brady violation, the Agurs Court ruled that convictions based on the knowing use of perjured testimony could be overturned only if there is a “reasonable likelihood” that the false testimony affected the verdict. Id. at 103, 96 S.Ct. 2392; accord Kyles, 514 U.S. at 433 n. 7, 115 S.Ct. 1555. If courts must scrutinize the knowing use of perjured testimony under this standard, there is no principled justification for treating the government more harshly (such as by interposition of the Larrison rule) when its use of perjured testimony is inadvertent.

By and large, the courts that apply a possibility standard when the government unwittingly has used perjured testimony have not addressed this concern, presumably because each of those three circuits committed itself to the Larrison rule prior to the date (June 24, 1976) that the Court decided Agurs. See, e.g., Wallace, 528 F.2d at 866 (decided Jan. 8, 1976); Gordon, 178 F.2d at 900 (decided Dec. 5, 1949); Larrison, 24 F.2d at 87 (decided Jan. 7, 1928). Before Agurs, the Second Circuit stood alone in its stinging critique of Larrison and its concomitant rejection of the possibility standard. See Stofsky, 527 F.2d at 245-46 (decided Nov. 7, 1975). Agurs transformed the legal landscape and marked the start of what has become an unmistakable trend toward use of the probability standard. See, e.g., Torres, 128 F.3d at 49; Sinclair, 109 F.3d at 1531-32; Tierney, 947 F.2d at 860-61; Krasny, 607 F.2d at 844-45.

We also find significant the prevalence of probability-based rubrics in the Supreme Court’s criminal jurisprudence. This may be in part because probability standards serve courts’ institutional efforts to balance competing interests. The Justices have demonstrated their commitment to the use of probability benchmarks virtually across the board, save only in cases involving constitutional violations, see, e.g., Neder v. United States, — U.S. -, 119 S.Ct. 1827, 1837, 144 L.Ed.2d 35 (1999); Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), or the most basic structural errors, see, e.g., Johnson v. United States, 520 U.S. 461, 468-69, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (citing cases). See, e.g., Jones v. United States, — U.S. -, 119 S.Ct. 2090, 2102-03, 144 L.Ed.2d 370 (1999); Strickler v. Greene, — U.S. -, 119 S.Ct. 1936, 1948, 144 L.Ed.2d 286 (1999); Buchanan v. Angelone, 522 U.S. 269, 118 S.Ct. 757, 763, 139 L.Ed.2d 702 (1998); Schlup v. Delo, 513 U.S. 298, 326-27, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995); Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990); United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985); Strickland v. Washington, 466 U.S. 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984); Napue v. Illinois, 360 U.S. 264, 269-71, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959); Kotteakos v. United States, 328 U.S. 750, 764-65, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). Based on this extensive case law, it would be anomalous to establish a threshold lower than the probability standard for granting a new trial when a defendant discovers that his conviction was based in part on the government’s unknowing use of false testimony. And we would find it particularly disquieting to abandon so sensible a standard in favor of the Larrison rule, which casts a leaden weight on the scales and severely hampers efforts at nuanced, case-by-case evaluation.

To sum up, there is simply no reasoned basis for sui generis treatment of newly discovered perjury—at least in circumstances in which the government’s use of the tainted testimony was unwitting. Accordingly, we hold that when a defendant grounds a motion for a new trial in a criminal case on a claim that he has newly discovered perjury on the part of one or more government witnesses, the conviction nonetheless should stand unless the force of the newly discovered event (i.e., the fact and nature of the perjury) and the content of the corrected testimony are such that an acquittal probably would result upon retrial.

Before leaving our discourse on the applicable standard, a caveat is in order. It should be clearly understood that this discussion deals with the government’s un-tvitting use of perjured testimony. We except from our holding situations in which the government’s use of perjured testimony was not unwitting. Although we leave the question of what standard then applies for another day, we note that some courts which apply the probability standard to situations involving the government’s innocent use of perjured testimony opt for a different standard when the government’s use of the perjured testimony is knowing or reckless. See, e.g., Torres, 128 F.3d at 49; Tierney, 947 F.2d at 860-61; see also Sinclair, 109 F.3d at 1532 (refusing to foreclose use of the possibility standard in such circumstances).

Having set the standard, we proceed to consider the specific attributes of the case at hand. The district court found that the newly discovered evidence to which the appellant adverted was both unknown to him and material, and that the appellant had exercised due diligence in respect thereto. See Huddleston, 23 F.Supp.2d at 74-75. The court also found that the prosecutor did not know at the time of trial that Chago and Gonzo had assumed bogus identities and were testifying falsely. See id. at 75. The appellant does not seriously contest this finding. The fate of the motion hinged, therefore, on an application of the probability standard. This means that the appellant had the burden of showing that the event and the content of Chago’s and Gonzo’s mendacity, viewed alongside the corrected testimony, probably would lead a jury to acquit him the second time around. The district court concluded that the appellant failed to make this showing and denied the motion for a new trial. See id. at 78-79. We discern no abuse of discretion.

We need not tarry. The record makes manifest that the jury had ample evidence of the appellant’s guilt: he incriminated himself over and over again during his taped telephone conversations with Gonzo; he appeared at the appointed time and place for the planned drug buy; and he made several damning admissions to various officers immediately following his arrest. Against this backdrop, it is hard to envision any realistic likelihood that, armed with knowledge of Chago’s and Gonzo’s perjury and the content of their statements, a fresh jury would credit the appellant’s far-fetched tale and vote to ae-quit.

B. Disclosure.

From the time of their arrests and throughout their own trials, Chago and Gonzo held themselves out to the authorities as Puerto Ricans. Both before and during the appellant’s trial, the prosecution did not know that these witnesses had assumed bogus identities and that their representations were apocryphal. It did, however, know the appellant’s theory of the case, i.e., that the three men were engaged in a legitimate venture to export goods to the Dominican Republic, and that, when the relationship soured, Huddleston sojourned to the Burger King restaurant solely to recover some belongings that he had loaned to his erstwhile associates. Despite this knowledge, the government did not divulge in advance of trial that Chago and Gonzo purported to be Puerto Rican. See Herrara-Sarita, 1999 WL 525924, at *1, *3; Huddleston, 23 F.Supp.2d at 75. The appellant strives to persuade us that a new trial is warranted because this omission transgressed the principles enunciated in Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We are unconvinced.

Brady holds, in essence, that the government has an obligation to disclose to the accused in advance of trial favorable, exculpatory evidence in its possession. See id. The duty to disclose such evidence attaches even absent the accused’s request for it. See Agurs, 427 U.S. at 107, 96 S.Ct. 2392. Moreover, the duty extends to impeachment evidence as well as to exculpatory evidence per se. See Strickler, 119 S.Ct. at 1948 & n. 21; Bagley, 473 U.S. at 676, 105 S.Ct. 3375; Giglio v. United States, 405 U.S. 150, 154-55, 92 5.Ct. 763, 31 L.Ed.2d 104 (1971); United States v. Devin, 918 F.2d 280, 289 (1st Cir.1990).

Seizing on this obligation, the appellant argues that the government knew that Chago and Gonzo were claiming to be from Puerto Rico and should have realized that this information was material to his defense. According to the appellant, he had a legitimate reason for associating with Chago and Gonzo—a plan to open an export business to the Dominican Republic—■ and their claims of Puerto Rican background constituted salient evidence because they claimed to be Dominican while they were dealing with him.

Strictly speaking, the information concerning Chago’s and Gonzo’s claim of Puerto Rican origin is not exculpatory because it has no real bearing on the appellant’s guilt. Their claim diminishes neither the force of the government’s case nor the strength of the appellant’s explanation. The appellant argues, however, that Cha-go’s and Gonzo’s claims constitute impeachment evidence under Giglio.

Assuming, arguendo, that the appellant is correct, the withholding of exculpatory or impeachment evidence does not warrant reversal except upon a showing of prejudice, that is, unless there is a “reasonable probability that the suppressed evidence would have produced a different verdict.” Strickler, 119 S.Ct. at 1948. In this context, “reasonable probability” means a probability sufficient to undermine confidence in the outcome. See Bagley, 473 U.S. at 682, 105 S.Ct. 3375. The witnesses’ claims to be Puerto Rican do not pass through this screen. See Strickler, 119 S.Ct. at 1948.

Moreover, as the district court noted, even if the professions of Puerto Rican background had been disclosed in advance of trial, the notion that the appellant’s counsel would have been able to gather enough information to attack the identity of Chago or Gonzo directly is “20/20 hindsight.” Huddleston, 23 F.Supp.2d at 76. The probation officer learned the truth only after exhaustively investigating data provided by his Puerto Rican counterparts and the Social Security Administration in the course of preparing presentence reports for Chago and Gonzo. See Herrara-Sarita, 1999 WL 525924, at *1. It would be surprising if the appellant’s counsel could have brought such resources to bear on the issue.

We have said enough on this score. We conclude, without serious question, that even if the witnesses’ feigned adoptions of Puerto Rican heritage constituted impeachment evidence under Giglio, the appellant is not entitled to a new trial because he was not prejudiced by the non-receipt of this information.

C. Sentencing.

The appellant’s final assignment of error implicates his sentence. In narcotics cases, drug quantity is an important integer in the sentencing calculus. See, e.g., United States v. Marrero-Ortiz, 160 F.3d 768, 779 (1st Cir.1998); United States v. Sepulveda, 15 F.3d 1161, 1196-97 (1st Cir.1993). In this instance, the sentencing court determined that the appellant bore responsibility for between 50 and 100 grams of cocaine. See USSG § 2Dl.l(c)(12) (placing at least 50 grams but less than ' 100 grams of cocaine at offense level 16). The appellant maintains that the court erred in making this computation because it placed undue reliance on improper and incredible testimony.

The facts are as follows. When the government learned that Chago and Gonzo had committed perjury, it elected to present other evidence of drug quantity at the disposition hearing. To this end, the government called as a witness Jamie Morel, the appellant’s former supplier and the initial liaison between him and Chago. Morel testified to various narcotics transactions between Chago and the appellant. After hearing this evidence and pondering the trial testimony, the court concluded that, at a minimum, the appellant bore responsibility for 28.35 grams of cocaine that he had expected to obtain at the restaurant and for at least two deliveries of 14 grams apiece that Chago had made. Because the latter finding was based largely on Morel’s testimony, the appellant contests it.

We review the district court’s findings of fact with respect to drug quantity' for clear error. See United States v. Sklar, 920 F.2d 107, 110-11 (1st Cir.1990). We see none here. The drug quantity properly attributable to a defendant is not limited to the drugs involved in the offense of conviction. See United States v. Graciani, 61 F.3d 70, 74 (1st Cir.1995); Sklar, 920 F.2d at 110-11; see also USSG § lB1.3(a)(2) (explaining concept of “relevant conduct”). On this record, the court was entitled to find that Morel had firsthand knowledge of the appellant’s relevant conduct; that he had supplied the appellant with cocaine in the past and had facilitated an arrangement whereby his associate (Chago) became the appellant’s primary source of supply; and that this arrangement lasted until Gonzo succeeded Chago as the appellant’s supplier. Given this continuous chain, it was not clear error for the district court to credit Morel’s testimony. See United States v. Eke, 117 F.3d 19, 23-24 (1st Cir.), cert. denied, 522 U.S. 1034, 118 S.Ct. 639, 139 L.Ed.2d 617 (1997) and 522 U.S. 1066, 118 S.Ct. 732, 139 L.Ed.2d 670 (1998); Natanel, 938 F.2d at 312-13.

To be sure, the appellant argues that Morel’s testimony regarding dates and times was fuzzy, and that the court therefore should have disregarded it. But the purport of Morel’s testimony was nose-on-the-face plain, and the carping about details amounts to nothing more than an attack on Morel’s credibility. We have said with echolalic regularity that “[s]uch credibility calls are grist for the trial court’s mill.” Sepulveda, 15 F.3d at 1198. Notwithstanding some minor discrepancies in Morel’s testimony, “we do not think it unreasonable ... to believe that the testimony of a man experienced in drug deals was sufficient to establish an appropriate drug quantity.” Natanel, 938 F.2d at 312-13.

The appropriateness of the court’s reliance on Morel’s testimony dooms the .appellant’s drug quantity challenge. An approximation of drug quantity will be upheld “as long as it represents a reasoned estimate of quantity.” United States v. Webster, 54 F.3d 1, 5 (1st Cir.1995). The determined drug quantity figure must be supported only by a preponderance of the evidence. See Sepulveda, 15 F.3d at 1198. The government met that benchmark here. Morel’s testimony jibed with the trial testimony of Chago and Gonzo in relevant respects, and although these witnesses had perjured themselves as to certain matters, the court nevertheless remained free to credit their testimony concerning the amounts of cocaine they had supplied to Huddleston. See Webster, 54 F.3d at 5 (upholding district court’s decision to credit testimony at sentencing from “an admitted perjurer, a drug user, and a turncoat, who received a substantially reduced sentence for implicating others”); United States v. Indelicato, 97 F.3d 627, 632 (1st Cir.1996) (“[Credibility judgments at sentencing are the trial judge’s province, and the fact that the district judge rejected some of [the witness’s] testimony as not credible does not mean that she could not credit other aspects of his testimony.” (citation omitted)), cert. denied, 519 U.S. 1140, 117 S.Ct. 1013, 136 L.Ed.2d 890 (1997).

We need go no further. The district court made a reasoned approximation of drug quantity, well supported by a preponderance of the evidence. No more was exigible.

Affirmed. 
      
      . Even on his own testimony, the appellant did not have a plean bill of health. He admitted that he had received cocaine from Chago (asserting, however, that he accepted the contraband as payment for automotive repair work). He also admitted that he had purchased cocaine from both Chago and Gonzo on occasion for personal use.
     
      
      . See, e.g., United States v. Sepulveda, 15 F.3d 1216, 1221 & n. 7 (1st Cir.1993) (‘'assuming]” for argument's sake that Larrison applied and finding that a new trial was not required); Natanel, 938 F.2d at 313 (mentioning Larrison, noting that the question of its validity was open, and finding no need to resolve that question); United States v. Wright, 625 F.2d 1017, 1020 (1st Cir.1980) (stating that the Larrison rule was "arguably applicable,” but noting that this circuit had not yet decided the validity of the rule, and leaving the issue unresolved); Pelegrina v. United States, 601 F.2d 18, 21 (1st Cir.1979) (referring to the Larrison rule, but finding it “not applicable”).
     
      
      . Some courts (including a few courts that reject the Larrison rule) nonetheless follow Larrison's lead in mounting a harmlessness inquiry and focus on whether the jury in the original trial would have acquitted absent the false testimony. See, e.g., Torres, 128 F.3d at 49. Others peer ahead, predicting the likelihood vel non that an acquittal would result on retrial. See, e.g., Tierney, 947 F.2d at 861. We have used the latter approach here, as we deem it potentially most helpful to the appellant on the particular facts. But in this case, all roads lead to Rome — so we leave for another day the relative soundness of these divergent approaches. Indeed, it may be that a flexible standard is more desirable than any fixed one, leaving courts the discretion to select the temporal focus that best fits the circumstances of a given case.
     
      
      . The government did not possess information about the identities of Chago and Gonzo until after the Huddleston trial, so only their claims of Puerto Rican background are at issue here. See Huddleston, 23 F.Supp.2d at 75-76.
     
      
      . As the district court sagaciously noted, impeaching Chago and Gonzo with their claims of Puerto Rican background might have backfired inasmuch as no one knew at the time of trial that the claims were false, and the information would have undercut the appellant's assertion that he associated with Chago and Gonzo because he hoped to start a legitimate business oriented to the Dominican Republic. See Huddleston, 23 F.Supp.2d at 76.
     
      
      . In the circumstances presented here, the reasonable probability standard is appropriate because the appellant’s contention is that the government withheld impeachment evidence—the pretrial professions of Puerto Ri-can background—that would have been useful to the defense at trial. See Kyles, 514 U.S. at 433-34, 115 S.Ct. 1555.
      
     