VAN GRAAFEILAND, Circuit Judge:

George Pape appeals from a judgment of the United States District Court for the Eastern District of New York (Glasser, J.) convicting him of endeavoring to obstruct justice, 18 U.S.C. § 1503, and of conspiring to do so, 18 U.S.C. § 371. For the reasons that follow, we affirm.

The instant case arises from Pape's service as a juror in United States v. John Gotti et al., No. 85 CR 178 (EHN) (E.D.N.Y. 1987) [hereinafter "the Gotti trial"]. In that case, John Gotti, the reputed head of the Gambino Organized Crime Family of La Cosa Nostra, and seven co-defendants were tried on criminal RICO charges, based on alleged predicate acts of loan sharking, gambling, armed robbery and murder.

Jury selection in the Gotti trial commenced in April 1986 before United States District Judge Eugene H. Nickerson. When it became apparent that virtually all jurors were being excused, however, Judge Nickerson suspended the proceedings and instituted anonymous selection procedures. These procedures required that several hundred prospective jurors fill out detailed, twenty-two page questionnaires and appear individually before Judge Nickerson for additional voir dire. A jury finally was selected in September 1986, with defendant seated as Juror Number 11. Following the acquittal of Gotti and his seven co-defendants, Pape was indicted for participation in a scheme to accept money in exchange for voting to acquit.

Prior to indicting Pape, the Government interviewed most of the former Gotti jurors. The Government conducted the first of these interviews prior to informing the court or seeking permission to engage in this practice. The remaining interviews were conducted after receiving court permission, but without court supervision or circumscription.

Following Pape's indictment, he moved the court for permission to interview the former jurors. In a series of pretrial rulings, Judge Glasser ordered that all jurors be approached by means of a letter sent from the court. Pape's counsel was permitted to interview only consenting jurors, and then only in Judge Glasser's presence. Prior to the interviews, the court reviewed the questions proposed to be put to the jurors, and excluded those that were not addressed to the charges in the indictment. Defendant was able to interview three jurors shortly before his trial.

At the trial, the Government introduced the testimony of one Salvatore Gravano. Gravano, indicted after the Gotti trial for his activities as underboss of the Gambino family, took the stand as a cooperating witness. He testified that Bosko Radonjich approached him shortly after the Gotti trial commenced and said that he "had a juror" who would cooperate for money by both voting to acquit and influencing his fellow jurors to do the same. At that time, Radonjich was the head of a gang called the "Westies," which had frequent illegal business dealings with the Gambino family. Though named as a defendant in the instant case, Radonjich has fled to Yugoslavia to avoid prosecution on other criminal charges.

Gravano testified that Radonjich informed him the cooperating juror was a long-standing friend. Gravano gave Radonjich $60,000 to reimburse him for payments to the juror to secure his not-guilty vote. After the Gotti trial, Radonjich asked Gravano to procure a job for the juror. Gravano declined, since to do so might have raised suspicion that the Gotti trial was rigged. Gravano never met Radonjich's juror.

At trial, it was established that Pape was both a close friend and long-time business associate of Radonjich. Pape admitted to meeting with Radonjich throughout the trial for lunch and dinner. He testified that following the trial, he requested that Radonjich secure him a job. No job ever materialized. During the FBI investigation of Pape's possible involvement, he initially denied discussing the trial with Radonjich. He subsequently retracted this statement, but insisted that no attempt to influence his vote had been made. Also admitted at trial was evidence that Pape had minimized or misrepresented the nature of his relationship with Radonjich during voir dire in the Gotti trial.

On appeal, Pape claims reversible error based on the district court's pretrial orders regulating the extent and manner of defense interviews of former jurors. He also challenges the sufficiency of the evidence to convict on both counts.

Pape argues that the district court committed constitutional error in limiting his access to the Gotti jurors. He contends that the district court erroneously applied Fed. R.Evid. 606(b) and unconstitutionally interfered with his Fifth and Sixth Amendment rights to present a defense and to call witnesses. Our review of the district court's rulings satisfies us that the court properly balanced the defendant's need to prepare a defense and the public's interest in maintaining the secrecy of jury deliberations.

Rule 606(b) provides, in pertinent part:

Upon an inquiry into the validity of a verdict or indictment, a juror may not testify as to any matter or statement occurring during the course of the jury's deliberations or to the effect of anything upon that or any other juror's mind or emotions as influencing the juror to assent to or dissent from the verdict or indictment or concerning the juror's mental processes in connection therewith, except that a juror may testify on the question whether extraneous prejudicial information was improperly brought to the jury's attention or whether any outside influence was improperly brought to bear upon any juror.

The rule by its terms applies only to inquiries concerning the validity of a verdict or indictment. It is a codified balancing of a defendant's right to a fair trial and an impartial jury against the public interest in maintaining both the finality of verdicts and full and free discussion within the confines of the jury room. See McDonald v. Pless, 238 U.S. 264, 267-68, 35 S.Ct. 783, 784, 59 L.Ed. 1300 (1915); Clark v. United States, 289 U.S. 1, 13-14, 53 S.Ct. 465, 469, 77 L.Ed. 993 (1933); United States v. Moten, 582 F.2d 654, 664 (2d Cir. 1978); Miller v. United States, 403 F.2d 77, 83 n. 11 (2d Cir. 1968).

Neither Pape nor the Government seeks to impeach the Gotti verdict. Nonetheless, a similar balancing of public and private interests is implicated. Pape claims the district court's rulings violated his right to present a defense and to call witnesses. However, these rights may yield to governmental interests and public policy in some situations. Roviaro v. United States, 353 U.S. 53, 60-62, 77 S.Ct. 623, 627-29, 1 L.Ed.2d 639 (1957); see also United States v. Valenzuela-Bernal, 458 U.S. 858, 102 S.Ct. 3440, 73 L.Ed.2d 1193 (1982). A defendant has a constitutional right of access to witnesses; he does not have a constitutional right of access to each and every witness he desires. United States v. Oliver, 908 F.2d 260, 262 (8th Cir. 1990).

We find no interference with Pape's right to present a defense that rises to the level of a constitutional violation. "[A] district judge has the power, and sometimes the duty, to order that all post-trial investigation of jurors shall be under his supervision." Moten, supra, 582 F.2d at 665. "[P]articularly in cases with semi-anonymous juries, such control would appear to be wise." United States v. Ianniello, 866 F.2d 540, 544 (2d Cir. 1989). Defendant was not barred completely from interviewing the former jurors. Cf. Moten, supra, 582 F.2d at 666. Limiting questioning to those jurors who come forward on their own is proper unless the district court determines, in its discretion, that more inquiry is necessary. Ianniello, supra, 866 F.2d at 544. This is especially so where, as here, the defendant was present during the very events concerning which he seeks discovery. In such a case, a defendant "can establish no Sixth Amendment violation without making some plausible explanation of the assistance he would have received" from the testimony of an unavailable witness. Valenzuela-Bernal, supra, 458 U.S. at 871, 102 S.Ct. at 3448; see also United States v. Bailey, 834 F.2d 218, 223-24 (1st Cir. 1987). In addition, the trial court is entitled, indeed encouraged, to limit the inquiry to those questions which may yield answers relevant to the asserted wrongdoing. Miller, supra, 403 F.2d at 83-84. Judge Glasser acted precisely within his appropriate role in allowing defense access to the former Gotti jurors within carefully circumscribed limits. See Moten, supra, 582 F.2d at 665-66.

Pape argues that the district court erred in not perceiving the difference in posture between a defendant seeking to impeach a guilty verdict and one seeking evidence for a forthcoming trial. We are not persuaded. As the district court clearly and correctly observed:

The indictment has nothing to do with impeaching the verdict. The indictment has to do with obstructing justice and endeavoring to improperly influence the jury. . . .

[M]y understanding of [the cases] is that they are not exclusively concerned with the implication of 606 of the Federal Rules of Evidence.

* * * * * *

[T]he jurors have a right to go home at the end of the trial . . . secure in the belief that they will not be harassed and they will not be questioned, and they have a right to return to the community and enjoy the privacy and anonymity that they enjoyed before they were summoned to serve as jurors.

In deciding in favor of the Government, we are not unaware that it failed to obtain court permission prior to its first interview of a former juror. "[N]otice to opposing counsel and the court should be given in all cases." Moten, supra, 582 F.2d at 666. However, in the instant case, no prejudice has been shown from the error. No material required to be revealed to the defendant under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), was discovered. In addition, defendant has failed to demonstrate the materiality of any "lost" testimony, and hence has shown no prejudice from this unequal treatment. Although Pape personally might not have been able to make the same detailed description of the deliberations that all the former jurors together might have provided, this does not relieve him of the duty to make some showing of materiality. See Valenzuela-Bernal, supra, 458 U.S. at 873, 102 S.Ct. at 3449. We, like the district court, are at a loss to determine what defendant expected to gain from further inquiry.

Defendant also challenges the sufficiency of the evidence establishing (i) his identity as the bribed juror, and (ii) an overt act within the five year period of the statute of limitations, 18 U.S.C. § 3282. A defendant challenging the sufficiency of the evidence bears a heavy burden. United States v. Medina, 944 F.2d 60, 66 (2d Cir. 1991), cert. denied, ___ U.S. ___, 112 S.Ct. 1508, 117 L.Ed.2d 646 (1992). A conviction will be upheld if, viewing the evidence in the light most favorable to the government, any rational juror could find the defendant guilty beyond a reasonable doubt. Id. (citing Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979)). Defendant has failed to meet that burden here.

Pape, unable to successfully challenge the proof that a conspiracy existed, contends that the evidence was insufficient to establish his identity as the bribed juror. We disagree. Once a conspiracy is shown to exist, the evidence sufficient to link a defendant to the conspiracy need not be overwhelming. See United States v. Ciambrone, 787 F.2d 799, 806 (2d Cir.), cert. denied, 479 U.S. 1017, 107 S.Ct. 668, 93 L.Ed.2d 720 (1986). In the instant case, there was evidence that Pape deceived the court during jury voir dire with respect to his relationship to Radonjich. In addition, Pape himself provided corroborating testimony tending to establish his identity as a co-conspirator. Pape testified that he met with Radonjich throughout the trial. While initially denying any discussion of the trial with Radonjich, Pape later admitted at least limited discussions. Pape also admitted that Radonjich tried to find him a job following the trial but failed. A jury is entitled to base its verdict on inferences drawn from circumstantial evidence. United States v. Roldan-Zapata, 916 F.2d 795, 802 (2d Cir. 1990), cert. denied, 499 U.S. 940, 111 S.Ct. 1397, 113 L.Ed.2d 453 (1991). Here, such evidence was sufficient to create a strong inference that Pape was indeed the bribed juror. The issue of identity was not the usual one of identifying a guilty person from among the public at large, but only from among the jurors at the Gotti trial. Furthermore, the deliberations of the Gotti jury and Pape's wrongful overt acts in connection therewith occurred within the period of the statute of limitations. See Fiswick v. United States, 329 U.S. 211, 216, 67 S.Ct. 224, 227, 91 L.Ed. 196 (1946).

Judgment affirmed.