Appellant Steve F. Giarratano was charged in a two-count indictment with mail fraud in violation of 18 U.S.C. §§ 1341 and 2.1 The jury returned a verdict of guilty on Count I and acquitted on Count II. Giarratano moved for a judgment of acquittal on Count I, which was granted on the basis that the evidence concerning the mailing related to Count I was not sufficient to support a finding of guilt. During the mail fraud trial, Giarratano took the stand in his own defense. Subsequently, he was indicted for perjury in violation of 18 U.S.C. § 1623 based on a portion of his testimony in the mail fraud trial.2 Giarratano moved to dismiss the indictment based on claims of double jeopardy and collateral estoppel. The district judge denied the motion. The jury found Giarratano guilty as charged.

Giarratano argues that his conviction should be reversed for three reasons: (1) the doctrine of collateral estoppel barred his trial for perjury; (2) the false statements for which he was convicted were immaterial to the issues raised in the mail fraud trial; and (3) the district court erred in refusing to grant the motion for a mistrial. We find no merit in these contentions.

First, Giarratano contends that his prosecution for perjury was barred by the doctrine of collateral estoppel because an element essential to the perjury conviction the unauthorized taking of money was decided in his favor in the mail fraud trial. In Ashe v. Swenson, 397 U.S. 436, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970), the Supreme Court held that the doctrine of collateral estoppel applies to criminal cases as part of the constitutional protection against double jeopardy, and that "when an issue of ultimate fact has once been determined by a valid and final judgment, that issue cannot again be litigated between the same parties in any future lawsuit," 397 U.S. at 443, 90 S.Ct. at 1194. In Johnson v. Estelle, 506 F.2d 347, 350 (5th Cir.), cert. denied, 422 U.S. 1024, 95 S.Ct. 2619, 45 L.Ed.2d 682 (1975), this court stated that application of the doctrine of collateral estoppel "depends upon whether some issue necessary for the prosecution's case in the second trial has necessarily been found for the defendant in the first trial." Where, however, "a 'rational jury' could have based its decision in the first trial on the State's failure to establish essential elements not in controversy in the second trial . . ., then the double jeopardy criterion would, of course, not apply." Id.3

Giarratano's collateral estoppel argument is meritless because the issue necessary for the prosecution's case in the second trial the taking of money to defraud was not necessarily decided for the defendant in the first trial. Indictment for mail fraud under 18 U.S.C. § 1341 requires (1) a scheme to defraud (2) that involves a use of the mails (3) for the purpose of executing the scheme. United States v. Kent, 608 F.2d 542, 545 (5th Cir. 1979); United States v. Knight, 607 F.2d 1172, 1175 (5th Cir. 1979). Thus, three facts were crucial to the Government's case on each count of mail fraud. With respect to Count I, the jury, in returning a verdict of guilty, necessarily decided the "scheme to defraud" issue against Giarratano. In granting the motion for judgment of acquittal on Count I, the trial judge specifically found that the proof of a mailing was insufficient. Thus, acquittal was granted by the trial court on the basis of an essential element not in controversy in the second trial. With respect to Count II, the jury returned a general verdict of acquittal. It is impossible to know with certainty the jury's basis for the acquittal, but absent any specific evidence to indicate that the jury's verdict was based on the "scheme to defraud" element of mail fraud,4 we conclude that the jury could have acquitted Giarratano because the Government failed to prove a mailing beyond a reasonable doubt. Thus, the issue of unauthorized payments to defraud was not necessarily decided in Giarratano's favor at the first trial.5

Second, Giarratano contends that one of the declarations which formed the basis of his perjury conviction was immaterial. On cross-examination by the Government in the mail fraud trial, Giarratano answered "no" when asked if the envelopes he received from Mr. Hudson's6 office contained any money. Giarratano argues that since the original indictment concerned unauthorized payments with respect to appraisals conducted on only two properties and that Mr. Hudson was not connected in any way with either transaction, Giarratano's answer to the question concerning payments from Mr. Hudson was immaterial to the prosecution's case in the mail fraud trial.

The government has the burden of proving the materiality of the false declaration. United States v. Damato, 554 F.2d 1371, 1373 (5th Cir. 1977). The test for materiality is a broad one whether the false testimony was capable of influencing the tribunal on the issue before it. United States v. Cosby, 601 F.2d 754, 756 (5th Cir. 1979); United States v. Cuesta, 597 F.2d 903, 921 (5th Cir.), cert. denied, 444 U.S. 964, 100 S.Ct. 451, 62 L.Ed.2d 377 (1979); United States v. Damato, 554 F.2d at 1372. Furthermore, we have held that "the statements need not be material to any particular issue but may be material to any proper matter of inquiry." United States v. Abrams, 568 F.2d 411, 420 (5th Cir.), cert. denied, 437 U.S. 903, 98 S.Ct. 3089, 57 L.Ed.2d 1133 (1978) (emphasis in original). See also United States v. Cosby, 601 F.2d at 756. Under these cases, it is clear that the declaration at issue is not immaterial merely because it does not directly concern one of the two transactions alleged in the mail fraud indictment. The question concerning payments by Mr. Hudson was within the proper scope of cross-examination under Fed.R.Evid. 611(b) since Giarratano had testified on direct examination that he had never accepted any unauthorized payment for an appraisal. Giarratano's denial that he received money from Hudson was clearly capable of influencing the jury on its decision concerning the offenses alleged in the indictment.7 Therefore, the trial judge properly ruled that the declaration was material.

Third, Giarratano argues that his conviction should be reversed because the district judge failed to grant a mistrial. During the perjury trial a juror, Mr. Trahant, notified the court that he had been a friend for several years of Mr. Dutreil, the husband of one of the Government witnesses. After questioning by counsel, Mr. Trahant was allowed to remain on the jury. However, later that same day an FBI agent was seen sitting with Mr. Dutreil. Because of this incident Mr. Trahant was excused and an alternate juror was seated. Defense counsel moved for a mistrial, which was denied.

"The settled rule in this and other circuits is that 'the trial judge, in his sound discretion, may remove a juror and replace him with an alternate juror whenever facts are presented which convince the trial judge that the juror's ability to perform his duty as a juror is impaired.' " United States v. Rodriguez, 573 F.2d 330, 332 (5th Cir. 1978), quoting United States v. Smith, 550 F.2d 277, 285 (5th Cir.), cert. denied, 434 U.S. 841, 98 S.Ct. 138, 54 L.Ed.2d 105 (1977) (emphasis in original). The trial court's exercise of discretion in replacing a juror "is not to be disturbed absent a showing of bias or prejudice to the defendant." United States v. Smith, 550 F.2d at 285. In our view, the trial judge's action fell well within the range of discretion afforded trial judges in issues of juror replacement. Further, Giarratano's only allegation of prejudice is that the substitution of another juror for Mr. Trahant changed "the entire composition of the jury." In the absence of a much more specific allegation of prejudice we cannot disturb the district judge's determination. Giarratano's contention that the incident involving the FBI agent was a deliberate attempt to influence juror Trahant in the Government's favor is likewise an unsupported, conclusory allegation. The trial judge found that the incident involved no deliberate misconduct by the Government, and Giarratano has presented no evidence contrary to the trial judge's determination. Therefore, we conclude that the trial judge did not err in refusing to grant the mistrial.

The judgment of the trial court is AFFIRMED.