
    UNITED STATES of America, Appellee, v. Eric C. PAYNE, Defendant-Appellant.
    No. 1558, Docket 94-1613.
    United States Court of Appeals, Second Circuit.
    Argued May 24, 1995.
    Decided Aug. 23, 1995.
    
      Michael S. Sommer, Asst. U.S. Atty., New York City (Mary Jo White, U.S. Atty., S.D.N.Y., Alexandra Rebay, Asst. U.S. Atty., New York City on the brief), for appellee.
    Louis R. Aidala, New York City, for defendant-appellant.
    Before: VAN GRAAFEILAND, Senior Circuit Judge, KEARSE, and CALABRESI, Circuit Judges.
   KEARSE, Circuit Judge:

Defendant Erie C. Payne appeals from a judgment entered in the United States District Court for the Southern District of New York, Charles S. Haight, Jr., Judge, convicting him on two counts of a four-count indictment, to wit, one count of conspiracy to distribute crack cocaine and other narcotics, in violation of 21 U.S.C. § 841 (1988 & Supp. V 1993) and id. § 846 (1988) (count 1), and one count of distribution and possession with intent to distribute crack on December 18, 1991, in violation of 21 U.S.C. §§ 841(a)(1) and 841(b)(1)(B), and 18 U.S.C. § 2 (1988) (count 3), and sentencing him principally to 210 months’ imprisonment, to be followed by a five-year period of supervised release. On appeal, Payne contends principally that he should have been granted a new trial because the government failed to produce evidence that could have been used to impeach the credibility of one of its key witnesses. He also challenges various aspects of sentencing. For the reasons that follow, we find no basis for reversal.

I. BACKGROUND

The present prosecution arose from an investigation by the United States Drug Enforcement Administration (“DEA”) into narcotics dealing from an apartment on Baltic Street in Brooklyn, New York (“apartment” or “Baltic apartment”). Between November 1991 and January 1992, DEA employed an informant with an extensive prior criminal record, Mike Soto, to make a series of narcotics purchases from persons operating in the apartment. In January 1992, several individuals other than Payne, all of whom eventually pleaded guilty to various federal or state charges, were arrested in the apartment by officers of the New York City Police Department (“NYPD”).

Payne was arrested by federal authorities in July 1992 and was prosecuted separately. He was charged on the conspiracy and distribution counts described above, and on two other counts of which he was acquitted, to wit, distributing and possessing crack with intent to distribute on December 3,1991, and carrying firearms in connection with drug trafficking. The government’s evidence at Payne’s trial included various physical evidence and the testimony of several witnesses, including Soto, DEA agent James Clifford, who supervised Soto’s undercover purchases, and Deanne Wilkerson, who was one of the seven arrested by NYPD in January 1992.

A. The Physical Evidence and the Testimony of Clifford and Soto

Clifford and Soto described a series of undercover purchases of crack by Soto, supervised by Clifford, at the Baltic apartment beginning in November 1991. The first such transaction involving Payne took place on December 3,1991. On that day, at Clifford’s direction, Soto telephoned the apartment and asked to buy three ounces of crack. The woman who answered the phone advised Soto that she would contact her supplier to obtain the requested amount. Thereafter, Clifford, conducting surveillance of the apartment building, observed Payne and another man enter the building, leave about 15 minutes later, and then return. On his second entry into the building, Payne was carrying an open red potato-chip bag, from which he was eating potato chips. Clifford searched Soto and equipped him with a concealed microcas-sette recorder and $2,850 in cash to pay for the crack. Soto then entered the building and emerged a short time later carrying a red potato-chip bag, which contained three ounces of crack. Soto testified at trial that he paid the $2,850 to Payne for the crack. The tape recorder malfunctioned, however, and Soto’s conversations inside the apartment were not recorded.

On December 18,1991, Soto, supervised by Clifford as before but equipped with a recorder that functioned, again purchased crack at the Baltic apartment. Soto testified that five persons, including Payne, Rafael (“Ralph”) Vargas, Sonia Rodriguez, and a woman he later learned was Wilkerson, were in the apartment. When Soto asked to purchase two ounces of crack, Payne pointed to some crack in a dish and responded that he had only Pk ounces, “a little more, a little less,” but that he was expecting to have more within hours. A tape recording admitted at trial included the following conversation:

Sonia: (U/I) so all that he was able to get was one-five.
ERic (Payne): Our man is, he’s late right now.
MiKE: Yeah.
SoNiA: [’] he’s ...
EriC: Can he wait?
MiKE: How long?
ERIC: How long before that meet? ... Tell him another, another hour, about two o’clock.
Mike: Huh?
Eric: Two o’clock.
MiKE: Two o’clock.
Eric: Right now, all I have is an ounce and change right now.
Mike: Oh, an ounce and change ... So, two o’clock you’ll have both of them.
Eric: Two o’clock I’ll try to have all of it. If I can’t have all of it, I’ll give you that right there. Make it two, two-thirty, whatever.
Ralph: So you want to come back at two Mike?
Mike: That’s what I’m gonna tell ’em yeah.
EriC: Ask him, ask him what’s the latest he can come back, the later the better, I ... better chance of me getting it. (U/ I).
Sonia: Tell him he has 45 minutes, alright?
Mike: And that’s what?
EriC: That’s one and a half, one and a quarter, something like that.
MiKE: Alright ... Okay.

After leaving the apartment and relating the substance of this conversation to Clifford and other agents, Soto, as instructed, called the apartment and told Wilkerson that he would wait until the full amount was available. Shortly thereafter, Clifford observed Payne and three others leave the building and drive away in a Cadillac.

Before Payne returned, Clifford reconsidered the decision to wait; he instructed Soto to return to the apartment and use the money he had been given to purchase the approximately Vk ounces of crack then available. Soto testified that when he returned to the apartment, Wilkerson pointed out a bag containing crack, and he took the bag and left $1900.

On leaving the building, Soto encountered Payne and Vargas, who had returned in the Cadillac. Soto recorded the ensuing sidewalk conversation:

EriC: You get it?
Mike: Yeah.
EriC: What happened, alright, my man ran out of this shit because he knows more than one people he deals with, so he just went to re-up.
Mike: Okay.
EriC: He won’t be back until after 4.
MiKE: Alright, I told her ...
Eric: Next time let me know way ahead of time so I can put some on the side for you.
Mike: I told him not two days ago, alright, but what I’ll do from now on is that the day before I’ll call in the morning.
ERIC: [Rjight.
Mike: Then you go all day and then the next day.
Eric: Alright.
Mike: But I’ll tell him on, uh, that to, uh, pick up the other half later.
Eric: Okay.
Mike: Alright.
Eric: After four.
MiKE: After four o’clock.
Eric: Yeah.
Mike: Always after four o’clock?
Eric: No, no, no, no just I’m saying that if you should want something more now, after four should be something here. But anytime, anytime.
Mike: Alright, anytime. Alright, alright (U/I) see you later.

Thereafter, Clifford directed Soto to return to the apartment to retrieve $350 of the $1900 Soto had left, representing the cost of the unpurchased half-ounce of crack. Soto testified that he returned to the apartment twice and on both occasions saw Payne counting money.

During the December 18 surveillance, Clifford took pictures of Soto, Vargas, and Payne as they conversed outside the building. One of the photographs was introduced at trial, and Soto and Clifford identified Payne in the photograph. The government also introduced tape-recordings of the two conversations Soto had recorded on December 18. Both Soto, who had dealt with Payne on December 3 and 18, and Clifford, who had conducted a postarrest interview of Payne, identified the voice of the dealer in the December 18 conversations as that of Payne.

In addition to the photograph and the tape-recordings, the government introduced, inter alia, the crack purchased in the apartment by Soto, and drug paraphernalia, cash, firearms and other narcotics seized from the apartment by NYPD in January 1992.

B. The Testimony of Wilkerson

Wilkerson testified that she faced a potential sentence of lijé to 13 years’ imprisonment and that she had entered into a cooperation agreement with the government, which would consider recommending a sentence reduction in exchange for, inter alia, her testimony against Payne. Her testimony with respect to Payne included the following.

In November 1991, Payne recruited Wilkerson to package crack that he would supply. She worked for Payne in a rented room in Brooklyn until early December 1991, when she relocated to the Baltic apartment. Thereafter, Wilkerson packaged crack and sold drugs supplied by several dealers, including Payne, who operated out of the apartment; each supplier generally took the proceeds from the sale of his own drugs. Wilkerson identified Payne as the dealer who supplied “[b]etween 85 and 90 percent” of the crack sold out of the apartment, bringing in as much as $1,000 to $2,000 per day.

Wilkerson testified that the crack sold to Soto on December 18 was supplied by Payne. Payne had instructed her by telephone that, if Soto elected to purchase the Vk ounces in the apartment, she should “tell Mike to leave the money.” She testified that Soto had come to the apartment and left cash in exchange for a bag that she “presumed” to contain drugs. Wilkerson further described Payne and others counting the money left by Soto, and stated that she had seen Soto return to the apartment once to retrieve the excess cash he had paid for the crack.

Wilkerson also, like Clifford and Soto, identified Payne in the December 18 photograph taken outside the apartment building and his voice in the tape-recordings of the two December 18 conversations. Wilkerson stated that the various firearms in the apartment belonged to Rodriguez and Vargas; she said she had never seen Payne in possession of any of the guns. Wilkerson testified that she had no involvement in the December 3 sale.

C. The Jury Verdicts and the Motion for a New Trial

Following four days of deliberations, the jury found Payne guilty on the conspiracy count (count 1) and the count charging distribution on December 18 (count 3). It acquitted him of distributing crack on December 3 (count 2) and of carrying firearms in connection with drug trafficking (count 4).

After the verdicts and prior to sentencing, Payne discovered that Wilkerson, prior to pleading guilty, had moved in the district court for various relief, supported by her affidavit dated May 5, 1992 (“Wilkerson affidavit” or “affidavit”). In that affidavit, Wilkerson had denied any involvement whatever in nareotics-related offenses. Paragraphs 2 and 3 stated:

2. That I never entered into a conspiracy to sell or possess narcotics with anyone.
3. That I never sold any narcotics from the apartment indicated in the indictment or anywhere else. So the statement that narcotics were purchased from me and for this untruth to be used in an application to obtain the search warrant was erroneous and the search warrant should be controverted.

Wilkerson’s pretrial motion was denied, and on the day before her trial was to begin, she pleaded guilty to (a) distribution and possession with intent to distribute crack on December 18, 1991, and (b) possession of firearms in connection with drug trafficking.

In advance of Payne’s trial, the government had furnished his counsel with, inter alia, (1) documents relating to Wilkerson’s arrest in the Baltic apartment, (2) NYPD reports relating to the investigation that led to Wilkerson’s arrest, (3) grand jury testimony and charging instruments pertaining to New York State charges filed against her, and (4) additional grand jury testimony and charging instruments pertaining to her federal indictment. The government had also produced Wilkerson’s plea and cooperation agreements with the government and a transcript of her plea allocution. However, the government failed either to furnish a copy of the Wilkerson affidavit or to alert Payne’s attorney to its presence in court files. Following his discovery of the affidavit, Payne moved for dismissal of counts 1 and 3 or, in the alternative, a new trial on those counts, contending that the government had failed to disclose material favorable evidence, thereby violating its obligations under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) (“Brady ”).

In a Memorandum Opinion and Order, 1994 WL 388948, dated July 19, 1994 (“July 19 Opinion”), the district court initially granted Payne’s motion for a new trial. The court concluded that the affidavit represented impeachment evidence that might have caused a “significant change” in the jury’s estimate of Wilkerson’s credibility. July 19 Opinion at 21. The court stated:

The picture she presented at trial was that of an innocent young woman working her way through school, who was seduced into the drug trade by a smooth talking Erie Payne. Indeed, during direct examination, the government had the witness repeatedly state that she had never sold drugs before her activities at the Apartment, and that it was the defendant who introduced her to the world of illicit drug sales....
Defense attorney [sic] engaged in a lengthy cross-examination of Wilkerson, where he attempted to demonstrate that her story was implausible. Other than to emphasize the benefits she stood to gain from her cooperation with the government, however, there was little basis for impeachment. I think it fair to say that defense counsel did not manage to portray Wilkerson as a person of questionable character.

Id. at 20. The court concluded that “[h]ad the jury been made aware that [Wilkerson] had previously submitted a false statement under oath denying the very acts to which she testified, her entire testimony might have been rejected by the jury.” Id. at 26.

The court rejected the government’s contention that any doubts sown by the affidavit as to Wilkerson’s credibility would not have undermined the other evidence and testimony inculpating Payne. It pointed out that with respect to the December 3 sale, both Clifford and Soto had given “detailed, plausible testimony ... identifying the defendant and describing his role in the sale,” and that the red potato-chip bag containing the crack purchased by Soto provided “physical evidence” corroborating their testimony. Id. at 22. Yet Wilkerson had given no testimony regarding that sale and the jury had acquitted. The court inferred “that the testimony of Clifford and Soto, when unsupported by Wilkerson, was for whatever reason (known only to the jury), insufficient to establish Payne’s guilt beyond a reasonable doubt.” Id. Thus, the court inferred that as to the December 18 sale as well, the testimony of Clifford and Soto alone was not sufficient to convince the jury, and the guilty verdict on that count must have “rested on Wilkerson’s testimony, the audiotape of the December 18th sale and the photograph taken by Clifford.” Id. at 23. The court continued:

[T]he evidentiary value of the tape and the photograph depended completely on Wilkerson’s testimony.
The audiotape of the December 18 sale contains numerous incriminating statements by the individual identified as Eric. Both Wilkerson and Soto testified that the voice identified in the transcript as “Eric” was the defendant’s. Wilkerson’s identification was based on her long-term relationship with the defendant, and Soto’s identification was based on his hearing the defendant speak on December 3rd and December 18th.
As noted, however, there is ample basis to infer that the jury did not regard Soto as credible. Payne did not testify, so the jury had no independent basis for determining whether the voice on the tape was his. Assuming that the jury disbelieved Soto, the only basis which the jury could have had for concluding that the voice on the tape was the defendant’s was Wilkerson’s testimony.
The government argues that the defendant was photographed having the conversation in question, and presumably, the jury could have concluded that the voice was Payne’s because the photograph shows him conversing with [Soto]. The photograph, however, does not solve the government’s problems. Taken at a considerable distance, it shows three individuals talking on the sidewalk. The person identified as Payne is shown in profile. It is impossible, however, to discern his features with any detail. One cannot even conclude with any certainty the race of the person identified as Payne.
As discussed above, Soto’s identification of the individual as Payne must be disregarded. It is unlikely that the jury could or did conclude the person in the photograph was the defendant, based only on its observation of the defendant over the course of a one week trial. The jury’s conclusion that the individual depicted in the photograph is the defendant most likely was based on Wilkerson’s identification, an identification based on a long relationship and her own participation in the activities of December 18th.
Accordingly, the government’s contention that Wilkerson’s testimony was corroborated by other independent evidence is inaccurate. At trial, Wilkerson identified Payne as the speaker on the tape and the figure in the photograph. Given the jury’s resolution of other disputed issues, Wilkerson’s testimony must be regarded as central to these questions of identification.

Id. at 23-25. In sum, the court concluded that ‘Wilkerson was the centerpiece of the government’s case with respect to the charges on which Payne was convicted.” Id. at 26.

The court also rejected the government’s contention that, because the Wilkerson affidavit was filed in a public court record accessible to Payne, the government had no obligation under Brady to produce the affidavit. The court concluded that Payne “was not put on notice that Wilkerson had filed a pre-trial motion,” and thus “was not informed of the essential facts that would [have] prompted] him” to investigate the record of Wilkerson’s prosecution. July 19 Opinion at 28. The government was therefore deemed to have failed to disclose the affidavit for purposes of Brady analysis.

The government moved for reconsideration. It argued that the July 19 Opinion had overlooked evidence — principally the testimony of Clifford — that was independent of Wilkerson’s testimony and demonstrated Payne’s guilt on the count focusing on the December 18 sale. Thus, the government contended that the court had failed to note that Clifford (1) gave significantly more detailed testimony about the December 18 sale than about the December 3 sale, (2) had interviewed Payne following his arrest, becoming familiar with his voice, and thereby positively identified Payne’s voice on the tape recordings of the December 18 conversations, and (3) had photographed Payne conversing with Soto outside of the apartment building and identified Payne in the photograph that was admitted at trial. The government argued that the court had erred in concluding that the testimony of Clifford and Soto, which the jury had found insufficient to prove Payne’s involvement in the December 3 sale, was no more probative with respect to the events of December 18.

In a Memorandum Opinion and Order, 1994 WL 419872, dated August 8, 1994 (“August 8 Opinion”), the district court -withdrew its earlier decision, agreeing with the government that the July 19 Opinion had “ignored the crucial differences” in Clifford’s testimony with respect to the two sales. August 8 Opinion at 5. It stated:

As to the December 3rd charge, [Clifford] could only testify as to who went in and out of the building where the transaction took place. On December 18th, by contrast, he was able to see much of the transaction taking place, and the tape recording of that conversation, which unarguably incriminated the defendant, was played for the jury.

Id. at 5-6. Although the court adhered to its earlier view that the jury had not found Soto’s testimony trustworthy, it concluded that the jury had found Clifford to be credible, and that “[assuming that the jury believed Clifford and disbelieved Soto, ... there was sufficient evidence to support defendant’s conviction on the December 18th charge, even disregarding the testimony provided by Deanne Wilkerson.” Id. at 4. Thus, the court stated:

I am no longer persuaded that ‘Wilkerson was the centerpiece of the ... government’s case with respect to the charges on which Payne was convicted.” July Opinion, at 26. Even assuming that the government had disclosed the Wilkerson affidavit, and defense counsel had skillfully used it to completely discredit Wilkerson as a witness, the result of the proceeding probably would have been the same.

August 8 Opinion at 6.

The jury’s verdicts on counts 1 and 3 were reinstated, and Payne was sentenced as indicated above.

II. DISCUSSION

On appeal, Payne principally pursues his contention that the government’s failure to disclose the Wilkerson affidavit violated its Brady obligations and deprived him of due process. He also makes several other arguments, including challenges to the determination of his sentence. We find his contentions unpersuasive.

A. The Brady Challenge

In order to establish a Brady violation, a defendant must show, inter alia, (1) that the government failed to disclose favorable evidence, and (2) that the evidence it “suppressed” was material. See Brady, 373 U.S. at 87, 83 S.Ct. at 1196-97; Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972). The government contends here that Payne made neither showing. Although we reject the government’s contention that it complied with its disclosure obligations, we agree that the nondisclosure does not warrant a new trial in this case.

1. Suppression

The government, while conceding that it was “at fault in neglecting to produce the [Wilkerson] affidavit” (government brief on appeal at 23), contends, in seeming contradiction to this concession, that it had no duty to disclose the affidavit to Payne because it was in public court records to which Payne had access. The government states that Payne knew that Wilkerson had initially maintained her innocence of the federal charges against her, and it argues that he thus should have explored the court file in Wilkerson’s case. Given the circumstances here, we reject the government’s argument.

Under Brady and its progeny, the government has an affirmative duty to disclose favorable evidence known to it, even if no specific disclosure request is made by the defense. See, e.g., Kyles v. Whitley, — U.S. —, —, —, 115 S.Ct. 1555, 1565, 1567-68, 131 L.Ed.2d 490 (1995); United States v. Agurs, 427 U.S. 97, 108-10, 96 S.Ct. 2392, 2399-2401, 49 L.Ed.2d 342 (1976). The individual prosecutor is presumed to have knowledge of all information gathered in connection with the government’s investigation. See Kyles v. Whitley, — U.S. at -, 115 S.Ct. at 1567 (“prosecutor has a duty to learn of any favorable evidence known to the others acting on the government’s behalf in the case, including the police”). Where the government’s suppression of evidence amounts to a denial of due process, the prosecutor’s good faith or lack of bad faith is irrelevant. See id. at-, 115 S.Ct. at 1567-68; Brady, 373 U.S. at 87, 83 S.Ct. at 1196-97.

Nonetheless, evidence is not considered to have been suppressed within the meaning of the Brady doctrine if the defendant or his attorney “ ‘either knew, or should have known, of the essential facts permitting him to take advantage of [that] evidence.’” United States v. Zackson, 6 F.3d 911, 918 (2d Cir.1993) (quoting United States v. LeRoy, 687 F.2d 610, 618 (2d Cir.1982), cert. denied, 459 U.S. 1174, 103 S.Ct. 823, 74 L.Ed.2d 1019 (1983)). Thus, where a defendant and his codefendant had agreed to share information about their respective cases, and the defendant’s attorney had made representations indicating his awareness of the codefendant’s cooperation with the prosecution, the government’s failure to disclose a government agent’s statements concerning the scope of that cooperation was not a suppression within the meaning of Brady. See United States v. Zackson, 6 F.3d at 919. See also United States v. Diaz, 922 F.2d 998, 1007 (2d Cir.1990) (no Brady violation by nondisclosure of witness’s testimony as to a fact within personal knowledge of defendant), cert. denied, 500 U.S. 925, 111 S.Ct. 2035, 114 L.Ed.2d 119 (1991); United States v. Esposito, 834 F.2d 272, 275 (2d Cir.1987) (no Brady violation where defendant had possession of transcripts containing the pertinent material). Documents that are part of public records are not deemed suppressed if defense counsel should know of them and fails to obtain them because of lack of diligence in his own investigation. See, e.g., United States v. Bermudez, 526 F.2d 89,100 (2d Cir.1975) (state’s investigative files were not suppressed since defense counsel, who represented one of the defendants in the state proceedings, could have discovered them “with the exercise of due diligence”), cert. denied, 425 U.S. 970, 96 S.Ct. 2166, 48 L.Ed.2d 793 (1976).

In the present case, the district court found that the Wilkerson affidavit had been suppressed within the meaning of Brady, and we agree. Clearly, the government knew of the affidavit; it was filed in the federal prosecution of Wilkerson. Further, the Assistant United States Attorney handling Payne’s prosecution had also prosecuted Wilkerson and had handled the government’s opposition to the pretrial motion in support of which the Wilkerson affidavit was filed. And, as discussed in Part II.A.2. below, it was clear that the affidavit contained evidence favorable to Payne’s defense.

Nor are we persuaded that the government’s duty to produce the Wilkerson affidavit was eliminated by that document’s availability in a public court file. We have seen in the record of the present case no indication that Payne’s counsel was aware of facts that would have required him to discover the affidavit through his own diligent investigation on behalf of his client. Although Payne was aware before his trial that Wilkerson had initially pleaded not guilty to charges directly relating to the December 18 sale, inter alia, and that she did not elect to plead guilty until the brink of her scheduled trial, he had no apparent reason to believe that Wilkerson had filed an affidavit containing sworn denials of her involvement in narcotics sales at the Baltic apartment.

Further, the government produced for Payne a large volume of other materials concerning Wilkerson, including numerous documents relating to the federal investigation and her prosecution. Included were publicly available court documents such as the transcript of Wilkerson’s plea allocution. A defendant receiving such documents from the government could reasonably assume that the court files did not include other undisclosed exculpatory and impeachment documents pertaining to Wilkerson, and certainly not an affidavit in which she outright contradicted the testimony she was certain to give at the trial of Payne.

We conclude that the district court correctly ruled that the government had suppressed the Wilkerson affidavit within the meaning of Brady.

2. The Materiality of the Suppressed Evidence

The government’s Brady obligation to disclose extends only to favorable evidence that is material. See 373 U.S. at 87, 83 S.Ct. at 1196-97. Materiality in this context is “a mixed question of law and fact.” United States v. Rivalta, 925 F.2d 596, 598 (2d Cir.), cert. denied, 502 U.S. 875, 112 S.Ct. 215, 116 L.Ed.2d 173 (1991). While the trial judge’s factual conclusions as to the effect of nondisclosure are ordinarily “entitled to great weight,” United States v. Provenzano, 615 F.2d 37, 49 (2d Cir.), cert. denied, 446 U.S. 953, 100 S.Ct. 2921, 64 L.Ed.2d 810 (1980), we conduct our own “ ‘independent examination’ ” of the record in determining whether the suppressed evidence is material, United States v. Rivalta, 925 F.2d at 597 (quoting United States v. Provenzano, 615 F.2d at 49).

Undisclosed “evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383, 87 L.Ed.2d 481 (1985) (opinion of Blackmun, J.); see id. at 685, 105 S.Ct. at 3385 (opinion of White, J.). A “reasonable probability” is “a probability sufficient to undermine confidence in the outcome” of the case, id. at 682, 105 S.Ct. at 3383 (opinion of Blackmun, J.); hence, the undisclosed evidence will be deemed material only if it “could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict.” Kyles v. Whitley, — U.S. at —, 115 S.Ct. at 1566. This standard does not mean that a defendant is required to show that the undisclosed evidence would have rendered the evidence as a whole insufficient to support a conviction, see id. (test of Brady materiality “is not a sufficiency of evidence test”), or that if timely disclosure had been made, acquittal would have been certain. But the defendant is required to show more than just that the error was not harmless beyond a reasonable doubt. See Kyles v. Whitley, — U.S. at —, 115 S.Ct. at 1566-67; see also United States v. Agurs, 427 U.S. at 112, 96 S.Ct. at 2401 (“the constitutional standard of materiality must impose a higher burden on the defendant” than “the customary harmless-error standard”).

The evidence whose disclosure is required under Brady may consist not only of exculpatory evidence but also of impeachment evidence, see Bagley, 473 U.S. at 676, 105 S.Ct. at 3380; Giglio v. United States, 405 U.S. at 154-55, 92 S.Ct. at 766; Tate v. Wood, 963 F.2d 20, 25 (2d Cir.1992), since “[t]he jury’s estimate of the truthfulness and reliability of a given witness may well be determinative of guilt or innocence Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217 (1959). In general, impeachment evidence has been found to be material where the witness at issue “supplied the only evidence linking the defendants) to the crime,” United States v. Petrillo, 821 F.2d 85, 90 (2d Cir.1987); see also Giglio v. United States, 405 U.S. at 154-55, 92 S.Ct. at 766 (Brady violation found where government failed to disclose promise not to prosecute cooperating witness on whom government’s case against defendant “almost entirely” depended), or where the likely impact on the witness’s credibility would have undermined a critical element of the prosecution’s case, see United States v. Badalamente, 507 F.2d 12, 17-18 (2d Cir.1974) (same re nondisclosure of “hysterical” letters that would have had “powerful adverse effect” on witness’s credibility, where that credibility was “crucial to the determination of [the defendant’s] guilt or innocence”), cert. denied, 421 U.S. 911, 95 S.Ct. 1565, 43 L.Ed.2d 776 (1975). In contrast, a new trial is generally not required when the testimony of the witness is “corroborated by other testimony,” United States v. Petrillo, 821 F.2d at 89, or when the suppressed impeachment evidence merely furnishes an additional basis on which to impeach a witness whose credibility has already been shown to be questionable, see, e.g., id. at 90; United States v. Rosner, 516 F.2d 269, 273-74 (2d Cir.1975), cert. denied, 427 U.S. 911, 96 S.Ct. 3198, 49 L.Ed.2d 1203 (1976); see also Giglio v. United States, 405 U.S. at 154, 92 S.Ct. at 766 (new trial not required where newly discovered evidence is merely “possibly useful to the defense but not likely to have changed the verdict”) (internal quotes omitted).

In the present case, the Wilkerson affidavit was clearly relevant. While we think it improbable that the jury would have believed that the disclaimers in the affidavit were true and her plea of guilty was false, the affidavit would have served as useful impeachment evidence with which to attack the credibility of her testimony against Payne. At trial, defense counsel focused on Wilkerson’s incentive to implicate Payne as a means of gaining the government’s support, pursuant to her cooperation agreement, for a lesser sentence in her own case. The affidavit would have added concrete evidence that, in an effort to avoid punishment, Wilkerson had previously lied under oath with respect to some of the very questions the jury was to decide. It is thus reasonably probable that, in the hands of skillful defense counsel, the Wilkerson affidavit would have had a negative impact on the jury’s willingness to rely on Wilkerson’s testimony in convicting Payne.

The question remains, however, whether that impact would likely have placed the government’s evidence against Payne in such a different light as to undermine our confidence in the outcome of the trial. We conclude that it would not. Wilkerson’s testimony was but a fraction of the evidence linking Payne to narcotics dealing at the Baltic apartment and to the crack sold on December 18. Her testimony that the crack was supplied by Payne was corroborated, for example, by Soto’s testimony that it was Payne who responded to Soto’s in-person request for two ounces, telling Soto how much was on hand and when more would be available. Similarly, Soto corroborated Wilkerson’s testimony that he returned to the apartment to retrieve his excess payment, and that Payne was among those counting the proceeds of the sale at that time. Further, even if, as the district court inferred, the jury entirely disregarded the testimony of Soto, there was strong physical evidence of Payne’s involvement in the December 18 sale, including the crack itself that was purchased by Soto, the photograph of Payne and Vargas conversing with Soto outside the apartment building, the incriminating tape-recording made during that photographed conversation, and the incriminating tape-recording made earlier that day inside the apartment. The recorded conversations plainly revealed Payne’s involvement both in the December 18 sale and in the drug-distribution conspiracy alleged in the indictment.

With respect to both of the tape-recordings, Payne’s voice was identified not only by Wilkerson and Soto, but also by Clifford. Clifford not only saw Payne talking to Soto, but later interviewed Payne and thereby became familiar with his voice. And though Payne points out that the photograph is not terribly clear, Clifford’s identification of Payne in the picture was not based solely on a viewing of the photograph. Rather it was based also on his presence at the time and his actual observation of Payne, whom he also saw on other occasions, as one of the participants.

Finally, we note that, as the district court ultimately concluded, the jury’s acquittal of Payne on the count relating to the December 3 sale does not warrant the inference that acceptance of Wilkerson’s testimony was essential to the jury’s finding of guilt with respect to the December 18 sale, for the evidence with respect to the December 3 sale was far more circumstantial. Clifford could testify only that he saw Payne, carrying a red potato-chip bag, enter the apartment building, and that shortly thereafter, Soto entered the building and emerged with the same type of bag containing three ounces of crack. There was no photograph; there were no recordings of incriminating statements.

We conclude that the jury’s verdict that Payne had distributed crack, or aided and abetted its distribution, on December 18, and that he was a participant in a drug-distribution conspiracy, undoubtedly was not based on Wilkerson’s testimony alone. The other evidence of Payne’s guilt on those charges was sufficiently strong that the elimination of her testimony does not undermine our confidence in the outcome of the trial. We conclude, therefore, that Wilkerson’s affidavit was not material within the meaning of Brady.

B. The Sentencing Issues

Payne also challenges the district court’s calculation of his sentence under the federal Sentencing Guidelines (“Guidelines”), contending (1) that basing his offense level on the full two ounces of crack negotiated on December 18 was error because Soto actually purchased only T% ounces; (2) that enhancing his offense level under § 3Bl.l(b) as a “manager or supervisor” was error because there was no evidence that he managed or supervised as many as five persons; and (3) that the Guidelines’ provision making one unit of crack cocaine the equivalent of 100 units of powder cocaine violates the Cruel and Unusual Punishments Clause of the Eighth Amendment. These contentions are merit-less.

Under Guidelines § 2D1.1, “[a] defendant convicted of a narcotics offense involving a transaction that was under negotiation but not completed should normally have his base offense level calculated on the basis of the quantity of narcotics that was under negotiation,” United States v. Stevens, 985 F.2d 1175, 1182-83 (2d Cir.1993) (interpreting identically worded predecessor section); see Guidelines § 2D1.1 Application Note 12 (“In an offense involving negotiation to traffic in a controlled substance, the weight under negotiation in an uncompleted distribution shall be used to calculate the applicable amount.”); United States v. Podlog, 35 F.3d 699, 708 (2d Cir.1994) (“notwithstanding varying amounts involved in the negotiations ..., it is the amount ultimately agreed upon that should be punished”), cert. denied, — U.S. —, 115 S.Ct. 954, 130 L.Ed.2d 897 (1995), unless the defendant “neither intended nor was able to produce that amount,” United States v. Alaga, 995 F.2d 380, 383 (2d Cir.1993), cert. denied, — U.S. —, 114 S.Ct. 886, 127 L.Ed.2d 80 (1994); see also United States v. Hendrickson, 26 F.3d 321, 331-32 (2d Cir.1994) (government bears burden of proving defendant’s intent and capability with respect to negotiated amount).

In the present case, the record included the taped conversations in which Payne clearly indicated that he intended to, and believed he could, supply the full two ounces of crack requested by Soto. When Soto initially asked in the apartment to purchase two ounces, Payne responded that he had only 1^ ounces on hand but was expecting to have more within hours. Thereafter, on the street, Payne told Soto, “if you should want something more now, after four [o’clock] should be something here.” These conversations clearly sufficed to support the district court’s findings that the sale of the l]é ounces was an uncompleted distribution, and that Payne’s base offense level should therefore be calculated with respect to the two-ounce negotiated amount.

Guidelines § 3Bl.l(b) directs the district court to increase the defendant’s offense level by three points “[i]f the defendant was a manager or supervisor ... and the criminal activity involved five or more participants or was otherwise extensive.” A defendant acts as a “manager or supervisor” of a criminal enterprise involving at least five participants if he “exercise[s] some degree of control over others involved in the commission of the offense,” United States v. Liebman, 40 F.3d 544, 548 (2d Cir.1994) (internal quotes omitted), or “play[s] a significant role in the decision to recruit or to supervise lower-level participants,” United States v. Greenfield, 44 F.3d 1141, 1147 (2d Cir.1995). Payne, relying on language in certain of our prior decisions loosely referring to § 3Bl.l(b) as “requirpng] a determination that [the defendant] supervised five or more participants in the criminal activity,” see, e.g., United States v. Liebman, 40 F.3d at 548, contends that § 3Bl.l(b) was inapplicable because the evidence did not show that he supervised five people. His reliance is misplaced. The requirements of § 3B 1.1(b) are met if the defendant was a manager or supervisor and the criminal activity itself involved at least five participants; the defendant need not be the manager of more than one other person. See Guidelines § 3B1.1 Application Note 2 (“To qualify for an adjustment under this section, the defendant must have been the ... manager[ ] or supervisor of one or more other participants.”) (emphasis added); see also United States v. McGuire, 957 F.2d 310, 316 (7th Cir.1992) (§ 3Bl.l(b) “requires only that a defendant was a manager ‘and the criminal activity involved five or more participants’ — not that a defendant managed, or controlled, the five or more participants”) (quoting § 3Bl.l(b)) (emphasis in McGuire). Liebman itself, which quoted § 3Bl.l(b) Application Note 2, was not concerned with whether all five participants had been supervised by the defendant but with whether in fact there were as many as five participants.

In the present ease, the requisite size of the criminal enterprise was shown by evidence that six individuals other than Payne had packaged and/or sold drugs in the Baltic apartment. The court’s finding that Payne was a manager or supervisor was supported by evidence that, inter alia, Payne had recruited Wilkerson and paid her and three others to sell his crack and that Payne was responsible for most of the crack sales at the apartment. The court’s enhancement of Payne’s offense level under § 3Bl.l(b) was proper.

Finally, we reject Payne’s contention that the treatment under Guidelines § 2Dl.l(c) of each unit of crack cocaine as the equivalent of 100 units of powder cocaine violates the Eighth Amendment’s proscription against cruel and unusual punishment. We have previously upheld the Guidelines’ 100-to-l sentencing ratio against challenge under the Equal Protection Clause, concluding that “the greater accessibility and addictiveness of crack” furnished a rational basis for Congress’s adoption of the harsher penalties. United States v. Stevens, 19 F.3d 93, 97 (2d Cir.1994); see also United States v. Moore, 54 F.3d 92, 96-99 (2d Cir.1995) (adoption of ratio did not evince discriminatory intent); United States v. Then, 56 F.3d 464, 466 (2d Cir.1995); but see id. at 466-69 (Calabresi, J., concurring) (noting that Sentencing Commission has proposed elimination of the 100-to-l ratio because of (a) scant evidence to support the notion that crack poses a substantially greater threat to society than does powder cocaine, (b) lack of justification for 100-to-l ratio, and (c) disparate impact of “exaggerated” ratio on racial minorities).

More recently, we have rejected an Eighth Amendment challenge to Congress’s statutory imposition of enhanced penalties for crack offenses under 21 U.S.C. § 841(b)(1), which also incorporates the 100-to-l equivalence of crack to powder cocaine. See United States v. Jackson, 59 F.3d 1421, 1424 (2d Cir.1995) (per curiam). See generally Harmelin v. Michigan, 501 U.S. 957, 994, 111 S.Ct. 2680, 2701, 115 L.Ed.2d 836 (1991) (mandatory life sentence without possibility of parole for cocaine possession was “not unusual in the constitutional sense”); United States v. Angulo-Lopez, 7 F.3d 1506,1510 (10th Cir.1993) (“[hjarsher penalties for crimes involving crack regularly survive” Eighth Amendment challenges), cert. denied, — U.S. —, 114 S.Ct. 1563, 128 L.Ed.2d 209 (1994). The Jackson court relied on the same rationale underlying our rejection of equal protection challenges to the 100-to-l ratio under the Guidelines in concluding that § 841(b)(1) did not violate the Eighth Amendment. That rationale also requires our rejection of the present Eighth Amendment challenge. Accord United States v. Simmons, 964 F.2d 763, 767 (8th Cir.), cert. denied, — U.S. —, 113 S.Ct. 632, 121 L.Ed.2d 563 (1992); United States v. Avant, 907 F.2d 623, 627 (6th Cir.1990).

CONCLUSION

We have considered all of Payne’s arguments on this appeal and have found in them no basis for reversal. The judgment of conviction is affirmed.  