Defendant-appellant James Saget appeals from a judgment of conviction entered on April 1, 2003, in the United States District Court for the Southern District of New York (Kaplan, J.), following a jury trial. Saget was convicted of one count of conspiracy, in violation of 18 U.S.C. § 371, to traffic in firearms in violation of 18 U.S.C. § 922(a)(1)(A) and to make false statements in connection with firearms trafficking in violation of 18 U.S.C. § 922(a)(6), as well as one count of firearms trafficking in violation of 18 U.S.C. § 922(a)(1)(A). Saget and a co-conspirator, both of whom had prior convictions that precluded them from purchasing firearms, developed a scheme in which they used straw purchasers — people without past convictions — to legally purchase firearms in Pennsylvania, which Saget and his accomplice then transported to New York for resale on the black market. The government’s case at trial was based on the testimony of three straw purchasers, Shirley Stinson, Vincent Pemberton, and Marybel Deleon, who testified as cooperating witnesses for the government, as well as the recorded statements of Saget’s co-conspirator, Shawn Beckham. On appeal, Saget argues that, inter alia, the government did not disclose in a timely manner material that it was required to disclose under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963); the district court committed reversible error in denying Saget’s request for a jury instruction on multiple conspiracies; and the court abused its discretion in indicating that it would permit the government to offer evidence that Saget had recently changed his appearance if Saget argued to the jury that the government’s witnesses had failed to identify him in the courtroom.1

*669Saget first argues that the government withheld disclosure of three pieces of allegedly exculpatory evidence in violation of its duty to disclose exculpatory evidence “in time for its effective use at trial,” see United States v. Coppa, 267 F.3d 132, 144 (2d Cir. 2001). In its disclosures pursuant to 18 U.S.C. § 3500, the government provided Saget with Stinson’s statement to the ATF, in which she made statements inconsistent with her trial testimony, and Pemberton’s statement to the ATF that Saget was 6'3" tall, when in reality he was only 5 TO". At trial, Saget learned from Pemberton that Pemberton’s statement that the “Little Shawnie” for whom he bought guns was not the same person as Saget’s co-conspirator, Shawn Beckham. Saget contends that this evidence was exculpatory, material, and not disclosed in time for him to take advantage of them at trial and that the tardy disclosures prejudiced his case. See Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (delineating elements of a Brady claim); Coppa, 267 F.3d at 140.

Even assuming that these materials were exculpatory or impeaching2 and that the government should have disclosed them sooner, however, Saget has not demonstrated that the tardy disclosure prejudiced him in any way. Saget was able to make extensive use of Stinson’s and Pemberton’s statements to the ATF in cross-examining both witnesses, and has not demonstrated that his cross-examination would have been any more effective had he received the materials earlier. Although Saget now asserts that if he had had these materials earlier, he could have successfully argued against the admission of Beck-ham’s recorded statements, he has not established that these materials cast any doubt on the probative value of Beckham’s statements.

Saget next argues that the district court committed reversible error in refusing to give the jury a multiple conspiracies charge. Although “where the proof is susceptible to the inference that there was more than one conspiracy, the question of whether one or more than one conspiracy has been established is a question of fact for a properly instructed jury,” the court need not give the jury a multiple conspiracies charge “if only one conspiracy has been alleged and proved.” United States v. Maldonado-Rivera, 922 F.2d 934, 962 (2d Cir. 1990) (internal quotation marks omitted). Here, the district court declined to give the requested charge on the ground that there was no evidence from which the jury reasonably could infer the existence of separate networks. We review this determination de novo, see United States v. Han, 230 F.3d 560, 565 (2d Cir. 2000), and find no error. Saget contends that the evidence that Pemberton had never met Beckham, had bought guns for a third party, and, unlike most of the other straw purchasers the co-conspirators used, was not a female exotic dancer, indicates that he was not part of the Saget-Beckham conspiracy to which most of the government’s proof pertained. The fact that one member of a conspiracy does not know some of its other members is insufficient to establish the existence of multiple conspiracies, however, see Maldonado-Rivera, 922 F.2d at 963, and Pemberton’s dealings with an unconnected third party do not disprove his involvement with Saget. Moreover, that Pemberton was not the conspiracy’s typical straw purchaser does not in itself establish that there was a Pemberton-Saget conspiracy that was sep*670arate from the Saget-Beckham conspiracy. The district court correctly determined that a multiple conspiracies charge was not warranted.

Finally, Saget asserts that the district court abused its discretion when it indicated that if Saget attempted to argue that the cooperating witnesses did not identify Saget in the courtroom, it would allow the government to introduce evidence that Saget had recently changed his appearance by wearing glasses. We review the district court’s ruling on admissibility for abuse of discretion. See United States v. Abreu, 342 F.3d 183, 190 (2d Cir. 2003). Saget contends that donning glasses does not change a person’s appearance, and the court therefore should have excluded the evidence of the new glasses as irrelevant. If Saget were to have argued to the jury that the government’s witnesses had failed to identify him, he would have put his physical appearance in issue, however, and evidence of a recent change in his appearance would become relevant. If the government had introduced the glasses into evidence, Saget would then have been free to argue to the jury that his new glasses did not significantly change his appearance. The district court therefore did not abuse its discretion in indicating that it would permit the introduction of the glasses into evidence.

The judgment of the district court is AFFIRMED for the reasons stated in this summary order and in our previously issued opinion in United States v. Saget, 377 F.3d 223 (2d Cir. 2004). The mandate in this case will be held pending the Supreme Court’s decisions in United States v. Booker, No. 04-104, and United States v. Fanfan, No. 04-105 2004 WL 2331491 (U.S. October 4, 2004). Should any party believe there is a need for the district court to exercise jurisdiction prior to the Supreme Court’s decisions, it may file a motion seeking issuance of the mandate in whole or in part. Although any petition for rehearing should be filed in the normal course pursuant to Rule 40 of the Federal Rules of Appellate Procedure, the court will not consider the waiver or substance of any issue concerning defendant’s sentence until after the Supreme Court’s decisions in Booker and Fanfan. In that regard, the parties will have until fourteen days following the Supreme Court’s decisions to file supplemental petitions for rehearing in light of Booker and Fanfan.