ALVIN B. RUBIN, Circuit Judge:
An intricate and clever scheme to defraud the Government of money asserted to be due for Medicare services resulted in a lengthy and complicated indictment, a protracted trial, and a verdict of guilty. The defendant seeks to overturn that verdict by charging a bevy of errors in the indictment and trial. Because we find his arguments without merit, or the errors asserted harmless beyond a reasonable doubt, we affirm.
Ernest Winkle and three co-defendants were charged with conspiring to defraud the United States by securing unlawful Medicare payments.1 In the same indictment, Winkle and two of the three co-defendants were named in 19 additional counts charging the submission to the Government of Medicare payment requests that contained fraudulent statements.2 Alan Colmar, a nursing home administrator who was charged only with conspiracy, pleaded guilty to a reduced charge after the jury selection process in this case had begun. After the trial of a second co-defendant was severed,3 and the substantive charges against the remaining co-defendant were dismissed, Winkle and Joseph DiStefa-no were tried together on the conspiracy count and on the substantive charges against Winkle alone. During the three-week trial the parties called nearly 60 witnesses. The jury was unable to reach a verdict on the conspiracy count, but convicted Winkle on all substantive counts.4 On the Government’s motion, the conspiracy count against Winkle was dismissed.5 We set forth below the complex facts of this case only in detail sufficient to make comprehensible our analysis of the relatively straightforward principles of law that result in the denial of the relief he seeks.
I.
Factual Background
The conspiracy charged by the Government had three aspects: first, the defendants initiated a sales scheme for a Tampa, Florida, medical laboratory under which physicians ordered lab tests, at no charge to their patients; the lab then charged Medicare and unlawfully remitted “interpreta[708]*708tion” or “consultation” fees to the referring physicians. Second, the defendants solicited and charged Medicare for the laboratory business of several chiropractors when they knew that those services for chiropractic physicians could not lawfully be charged to Medicare. Third, the defendants conducted a program of respiratory testing and inhalation therapy for nursing home patients, and billed Medicare for such tests and therapy, although no physician had determined that either the tests or therapy were medically necessary as required by the applicable statutes and regulations.6
The 19 substantive counts grew out of the defendants’ inhalation therapy program. Evidence showed that the defendant Winkle had submitted 19 Medicare out-patient billing forms, prepared by him or at his direction, for medically unnecessary therapy. The Government introduced the forms, each of which indicated a diagnosis of “upper respiratory infection” or “emphysema” that the treating physician, Dr. Alvarez, as a Government witness, denied making. Dr. Alvarez further testified that he had neither ordered nor given permission for either the tests or the therapy treatments in question.
II.
Sufficiency of the Indictment
The defendant urges that the court below erred in not dismissing the indictment because of a variety of alleged deficiencies.
Winkle argues, first, that the conspiracy count is impermissibly vague and, in violation of F.R.Cr.P., Rule 7(c)(1), does not afford “a plain, concise and definite written statement of the essential facts constituting the offense charged.” He further asserts that the indictment, in violation of Rule 7(c)(1), omits “the official or customary citation of the statute, rule, regulation or other provision of law which the defendant is alleged therein to have violated.”7
These contentions are frivolous. Count One specifically alleges a violation of Title 18, Section 371 of the United States Code, which proscribes any conspiracy to defraud the United States.8 There is no requirement that the fraud comprise conduct that could be held unlawful under some other statute or rule:
The statute is broad enough in its terms to include any conspiracy for the purpose of impairing, obstructing, or defeating the lawful function of any department of government.
Haas v. Henkel, 1910, 216 U.S. 462, 479, 30 S.Ct. 249, 254, 54 L.Ed. 569, 577; accord, United States v. Johnson, 1966, 383 U.S. 169, 172, 86 S.Ct. 749, 751, 15 L.Ed.2d 681, 684. It is essential only that an indictment under 18 U.S.C. § 371 “properly [charge] a conspiracy, and with the required specificity [allege] the culpable role” of each of the alleged conspirators. Dennis v. United States, 1966, 384 U.S. 855, 860, 86 S.Ct. 1840, 1844, 16 L.Ed.2d 973, 978.
The indictment before us clearly passes this test. It alleges that the object of the conspiracy to defraud was:
causing the payment of Medicare benefits under the provisions of Title XVIII of the Social Security Act, as amended (42 U.S.C. §§ 1801-1879 [1395 — 1395pp]), to be [709]*709made in amounts greater than the amounts which were properly payable and which excess payments were not authorized under Title XVIII of the Social Security Act.
It further elaborates that the defendants arranged reimbursement for “medically unnecessary lab tests” by Medicare,
when in fact that program authorizes payment and reimbursement as provided in Title XVIII of the Social Security Act, Sections 1861 and 1862(a)(1), for only those tests which are medically necessary.
Thus, even if reference to other statutes or rules, the contravention of which would constitute fraud, were necessary to complete a charge under 18 U.S.C. § 371, sufficient notice of the relevant statutes is afforded by this indictment. The thrust of the Government’s case was, in the instance of lab tests, that physicians ordered tests not properly related to their patients’ diagnosis or treatment,9 and, in the case of inhalation therapy, that Winkle charged for tests and treatments that physicians did not order at all. With respect to the latter, in particular, the defendant testified:
Well, we can’t do any testing and submit for payment to Medicare unless we did have a doctor’s order and that is also true of any treatments that would be instituted.
This is precisely the interpretation for which the Government argues. We cannot discern any undue vagueness in the indictment.
We must also reject Winkle’s argument that he would be prejudiced by a prosecution under any count of the indictment because the language of the indictment might be deemed to track either 18 U.S.C. § 1001 or 42 U.S.C. § 1395nn.10 The indictment specifically names the former statute as the rule of law on which the substantive counts rely. To the extent that [710]*710the same conduct could be punished under either statute, the choice lies within the discretion of the prosecutor. United States v. Chakamakis, 5 Cir. 1971, 4149 F.2d 315. Were the Government to attempt a second prosecution, under a different statute, for the same conduct at issue in this case, the defendant could properly raise a double jeopardy claim at that time. Absent a second prosecution, the defense is, of course, premature. The indictment is clear, concrete and specific; that is enough to meet the defendant’s challenge.
III.
Conduct of the Trial
The defendant urges that his convictions should be reversed because the trial judge erroneously excluded evidence favorable to the defendant, the trial judge erred in admitting evidence of similar wrongful acts, the judge erred in his rulings regarding the conduct of rebuttal and surrebuttal, and the judge erred in his instructions to the jury.
The defendant urges that the trial court erred in excluding as hearsay his renditions of conversations with his salesmen, Matthew Rackstein and Gerald Talty, with Drs. Nessan McCann, Frank Norton and Robert Moorehead, and with his wife, Leonarda Winkle; he would have contradicted their testimony regarding the same conversations, and, therefore, this was proper impeachment and should not have been excluded as hearsay. See F.R.Evid. Rule 801(c). See United States v. Palacios, 5 Cir. 1977, 556 F.2d 1359, 1362-63; United States v. Sisto, 5 Cir. 1976, 534 F.2d 616, 622-23 (dicta). (No argument is made that Winkle’s testimony was admissible for substantive purposes.) The legal proposition on which the assertion is based is correct; impeachment to demonstrate the untruth of a witness’ testimony is not excludable as hearsay because it is not offered primarily to prove the truth of the matter asserted, but to contradict the prior testimony. J. Weinstein & M. Berger, Weinstein’s Evidence, H 607[06] (1977). However, a crucial prerequisite to concluding that the ruling was erroneous is missing.
Rule 103(a)(2) of the Federal Rules of Evidence provides that error may not be based on a ruling excluding evidence unless “the substance of the evidence was made known to the court by offer or was apparent from the context within which questions were asked.” While some circuits have apparently taken a more lenient approach, e. g., Charter v. Chleborad, 8 Cir. 1977, 551 F.2d 246, 248-9, cert. denied, 434 U.S. 856, 98 S.Ct. 176, 54 L.Ed.2d 128, this circuit will not even consider the propriety of the decision to exclude the evidence at issue, if no offer of proof was made at trial. Mills v. Levy, 5 Cir. 1976, 537 F.2d 1331, 1333; United States v. Muncy, 5 Cir. 1976, 526 F.2d 1261, 1263. See also Elliott v. Maggiolo Corp. 2 Cir. 1975, 525 F.2d 439, 444; Nanda v. Ford Motor Co., 7 Cir. 1974, 509 F.2d 213, 223.
We do not require a formal proffer; but the proponent of excluded evidence must show in some fashion the substance of his proposed testimony. The defendant here gave no indication concerning what he would have testified or the manner in which his contradiction or denial of what had already been adduced would have been admissible or helpful. While the defendant was given the opportunity to do so, outside the presence of the jury, his counsel merely stated that Winkle would testify as to his version of the conversations that he had with Rackstein, Talty, McCann, Norton, Moorehead, and Mrs. Winkle. This was not sufficient to make known to the court the substance of the evidence. See J. Weinstein & M. Berger, Weinstein’s Evidence If 103[04] at 103-38 (1977); 10 Moore’s Federal Practice § 103.22 (2d ed. 1976). Because an adequate offer of proof was not made, we “may not” find error under Rule 103, as interpreted in this circuit. Moreover, an analysis of the evidence that had been admitted in the light of what Winkle proposed to say, so far as the record permits some kind of inference, fails to persuade us that the exclusion of the testimony was harmful. Rather than unduly prolong this [711]*711opinion, we have discussed each of the instances in the footnote.11
The trial judge excluded as irrelevant the defendant’s testimony regarding his interpretation of a Medicare publication, and his conversations and correspondence with various persons at the Social Security Administration Bureau of Health Insurance and the Florida Department of Health and Rehabilitative Services. The judge’s rulings on this evidence, as well as the proffered list of prevailing Medicare rates, were well within his discretion concerning questions of relevance. United States v. Bryant, 5 Cir. 1974, 490 F.2d 1372, 1378, cert. denied, 419 U.S. 832, 95 S.Ct. 57, 42 L.Ed.2d 58.
The court did not err in permitting the Government to introduce evidence of wrongful acts extrinsic to the immediate prosecution. The Government produced requisitions that were purportedly signed in 1972 by a Dr. William Braell of Elmira, N.Y. for two patients’ x-rays; attached were request forms for Medicare payments for the x-rays that had been mailed to Blue Cross. These forms indicated that the provider of services was Integrated Medical X-Ray Services, and the requests for pay[712]*712merit were signed “Ernest A. Winkle.” Dr. Braell testified that he had ordered neither x-ray, and that, in one instance, he had expressly declined to sign the form, which someone named Ernest Winkle had brought to him; he had refused because the person named on the form was not Dr. Braell’s patient. Dr. Braell’s signature on the second form was, according to Dr. Braell, not only forged, but misspelled. The Government subsequently called a former employee of the defendant, who testified that, to his personal knowledge, the defendant was president of Integrated Medical X-Ray Services up until at least two months prior to the submission of the forms in question to Blue Cross.
Rule 404 of the Federal Rules of Evidence permits the introduction of evidence of extrinsic acts to show intent and the absence of mistake or accident, issues squarely raised by Winkle’s defense. The evidence offered was relevant and, as the court properly determined, probative and not unfairly prejudicial, especially in view of the court’s limiting instructions. United States v. Beechum, 5 Cir. 1978, 582 F.2d 898 (en banc).
On rebuttal, the Government produced a therapist to rebut Mrs. Winkle’s testimony concerning the manner in which the diagnostic information reported on the billing forms was obtained, and a doctor to rebut testimony that blanket orders had been given to permit the respiratory testing of his patients.12 The testing and treatment of these patients were comprised only in the conspiracy count, although they might be considered evidence of extrinsic acts relevant to the issue of intent with respect to the substantive counts as well. The judge incorrectly overruled an objection to the doctor’s testifying with respect to the contents of the charts, notwithstanding the Government’s failure to produce the charts themselves, which concededly were available. F.R.Evid., Rule 1002. In view of the limited relevance of the witness’s testimony to the defendant’s convictions, and the content of his testimony, we are persuaded that the defendant’s inability to cross-examine the witness on the basis of the original charts was harmless beyond a reasonable doubt.
In the course of the first rebuttal witness’s testimony, he described an “incentive plan” for the respiratory therapists that Winkle allegedly put into effect although the therapists did not receive any money under the plan. The defense proffered further testimony by the defendant DiStefano tending to show that the plan was considered, but not put into effect. The court refused to permit such testimony in surre-buttal.
The scope of rebuttal testimony is ordinarily a matter to be left to the sound discretion of the trial judge. Geders v. United States, 1976, 425 U.S. 80, 86, 96 S.Ct. 1330, 1334, 47 L.Ed.2d 592, 598; United States v. Sadler, 5 Cir. 1974, 488 F.2d 434, 435, cert. denied, 417 U.S. 931, 94 S.Ct. 2642, 41 L.Ed.2d 234. In this case, the new issue raised on rebuttal was of tangential relevance. The proffered surrebuttal testimony was not entirely contradictory, and, indeed, the witness’s proffered testimony concerning the reason why an incentive plan was considered, i. e., the therapists thought the defendants’ lab was “making a tremendous amount of money” and they “wanted more,” would have been helpful to the Government. Under these circumstances, the judge’s ruling was not an abuse of discretion.
The defense also proffered in surrebuttal the further testimony of a therapist who had already appeared for the Government; her testimony with regard to the defendant’s representations vel non as to the existence of doctors’ orders for inhalation tests and therapy would not have been addressed to a new issue. The defense was itself not sure of what she would have said on the matter in dispute. Again, the denial of surrebuttal was not an abuse of discretion.
[713]*713The defense asserts that, in instructing the jury, the court invaded the jury’s province by stating that the statements made in the billing forms involved in Counts Two through Twenty were material. The requirement of materiality under the second, or “false statement” clause of 18 U.S.C. § 1001,13 is a judge-made limitation to insure the reasonable application of the statute. United States v. Beer, 5 Cir. 1975, 518 F.2d 168, 170. We have repeatedly viewed the question of materiality in a “false statement” prosecution as a question of law for determination by the court. United States v. Krause, 5 Cir. 1975, 507 F.2d 113, 118; cf. United States v. Crippen, 5 Cir. 1978, 570 F.2d 535, rehearing and rehearing en banc denied, 579 F.2d 340. United States v. Haynie, 5 Cir. 1978, 568 F.2d 1091; United States v. Beer, supra. Consequently, the instruction was proper.
We also find no reversible error in the court’s instructions on the relevant Medicare statutes and regulations. Although one or two phrases, if taken wholly out of context, might tend to mislead, the charges taken as a whole and read against the factual background of this case were proper. United States v. Wells, 5 Cir. 1975, 506 F.2d 924; United States v. Jackson, 5 Cir. 1972, 470 F.2d 684, cert. denied, 1973, 412 U.S. 951, 93 S.Ct. 3019, 37 L.Ed.2d 1004.
IV.
Jury Impropriety
The defendant finally asserts as error the court’s denial of his motion for a new trial based on alleged jury impropriety.
Voir dire of the jury began on Thursday, July 22, 1976. Alan Colmar, who had not yet pleaded guilty to any charge, was present before the jury. On July 23, Col-mar entered his plea. The trial began after the weekend. The judge inquired of counsel what, if anything, they wished the jury to be told concerning Colmar’s absence. The defense asked that nothing be said; the Government took no position. The jury was not told the reason for Colmar’s absence.
After the jury rendered its verdict, its foreman, a member of another state’s bar, telephoned Winkle’s trial counsel to discuss various aspects of the case in which he was interested. According to the trial counsel, the foreman told him that one juror, a barber named Shifler, had disclosed to the jury that he knew Colmar had pleaded guilty. Trial counsel discussed the development with Winkle, who, according to counsel, decided that he did not want to raise the issue in a motion for new trial for fear it would affect his sentencing. Consequently, trial counsel failed to mention the possible impropriety to the court.14
After the defendant was sentenced, trial counsel withdrew, and the defendant retained new counsel to handle his appeal. New counsel, upon learning of the possible impropriety, filed a motion of intention to interview the trial jurors. The court ordered that no interviews be held, but scheduled a hearing, at which it considered the testimony of trial counsel and of the jury foreman.
The foreman testified that, during the jury’s consideration of Count One, a woman juror named Marjorie Graham had said to the jury that Colmar had pleaded guilty. The foreman did not recall having heard any such statement from another juror. The defendant’s trial counsel recounted his version of his telephone conversation with the foreman, and the circumstances surrounding his failure to notify the court of the asserted impropriety.
The defendant moved for a new trial. The court supplemented its first hearing by taking the testimony, several weeks later, of Graham. She testified that she had “supposed” Colmar had pleaded guilty, but [714]*714did not recall saying so to the jury.15 The court denied Winkle’s new trial motion based on the hearing, his repeated instructions to the jury to avoid extrinsic influences on their deliberations, and the trial counsel’s ethical breach both in speaking to the jury foreman and in not reporting the incident to the court.16
The basic principles under which the question before us must be resolved are well-settled. In any trial, there is initially a presumption of jury impartiality; prejudice will not be presumed, but can be demonstrated by a defendant by a preponderance of credible evidence. United States v. Wayman, 5 Cir. 1975, 510 F.2d 1020, 1024, cert. denied, 423 U.S. 846, 96 S.Ct. 84, 46 L.Ed.2d 67. Such prejudice may be shown by evidence that extrinsic factual matter tainted the jury’s deliberations; any “prejudicial factual intrusion” denies a defendant his rights to trial by an impartial jury and to challenge the facts adverse to him that are made known to the jury. United States v. Howard, 5 Cir. 1975, 506 F.2d 865, 866; Remmer v. United States, 1954, 347 U.S. 227, 229, 74 S.Ct. 450, 451, 98 L.Ed. 654, 656.
Where a colorable showing of extrinsic influence appears, a court must investigate the asserted impropriety:
The evidentiary inquiry before the district court . . . must be limited to objective demonstration of extrinsic factual matter disclosed in the jury room. Having determined the precise quality of the jury breach, if any, the district court must then determine whether there was a reasonable possibility that the breach was prejudicial to the defendant. In this determination, prejudice will be assumed in the form of a rebuttable presumption, and the burden is on the Government to demonstrate the harmlessness of any breach to the defendant.
United States v. Howard, supra, 506 F.2d at 869. Thus, an adequate demonstration of extrinsic influence upon the jury overcomes the presumption of jury impartiality; it shifts the burden to the Government to demonstrate that the influence in question was not, in fact, prejudicial.
In the case before us, the record indicates that the fact of Colmar’s plea was published in a newspaper. Winkle’s trial counsel recalled that the foreman told him that the juror who knew of Colmar’s plea had read about it.17 At the hearing, the foreman could not recall the source from which the juror knew of Colmar’s plea.18 Given this evidence, and the failure of the trial judge to say so, we can neither conclude that he found no extrinsic influence to have existed nor rest our disposition on an assessment of such a finding.19 We thus assume that a jury breach occurred, and consider the question of prejudice.
The sole count on which Colmar was tried jointly with other people was the conspiracy count, on which he was not convicted. The jury foreman testified that the fact of Col-mar’s plea was discussed in relation to the [715]*715jury’s deliberations on that count. By contrast, the defendant Winkle was convicted of 19 substantive offenses, the evidence of which, both documentary and testimonial, was not only relatively discrete but damning. We fail to discern any genuine possibility of prejudice to the defendant in his trial on the substantive counts from the jury’s awareness, with respect to the conspiracy count, that he may have associated with a criminally tainted individual.
In United States v. Hansen, 5 Cir. 1977, 544 F.2d 778, we reversed the conviction of a defendant after the trial court informed the jury that his co-defendant had pleaded guilty; in Hansen, unlike this case, the jury had no previous knowledge that any co-defendant existed. We said:
The prejudice to the remaining parties who are charged with complicity in the acts of the self-confessed guilty participant is obvious.
Id., 544 F.2d at 780 (emphasis supplied). Here, Winkle was not found guilty on any count in which he was charged with “complicity in the acts of the self-confessed guilty participant,” Colmar. The jury breach created no apparent prejudice to the defendant Winkle.20
Because we find no insufficiency in the indictment, no harmful error at trial, and no prejudice accruing to Winkle from the uncontrolled presentation to the jury of an extrinsic fact, the convictions of the defendant are AFFIRMED.