JAMES DICKSON PHILLIPS, Circuit Judge:

Dr. Peter V. Alexander appeals from multiple convictions for mail fraud, 18 U.S.C. § 1341, submission of a false claim, 18 U.S.C. § 287, and making a materially false statement, 42 U.S.C. § 1396k in connection with the submission of medical insurance claims. We remand the case for reconsideration of the defendant's motion for new trial on the grounds of failure by the Government to produce Brady materials, and for such further proceedings as may then be warranted. Subject to that reconsideration, we affirm the convictions.

I

At relevant times, Dr. Alexander operated a medical practice in Virginia Beach, Virginia, specializing in gynecology and obstetrics. The charges against Dr. Alexander arose out of his dealings with three major health insurers: (1) the Civilian Health and Medical Program of the Uniformed Services (CHAMPUS); (2) Medicaid; and (3) Blue Cross/Blue Shield. In essence, the indictment alleges that, between May 15, 1978, and December 7, 1982, Alexander perpetrated a fraudulent scheme on these insurers which involved the following eight different "parts": (a) submitting duplicate claims for the same services to more than one insurer; (b) using the Current Procedural Terminology (CPT) codes to submit false claims to all three; (c) falsely claiming that certain services had been performed when in fact they had not been; (d) claiming to have performed pregnancy tests on women he knew to have been sterilized; (e) falsely claiming to have diagnosed illnesses in connection with routine office visits not compensable by CHAMPUS or Medicaid without such a diagnosis; (f) claiming higher fees from insured patients than from cash-paying patients; (g) falsely claiming to have rendered higher-compensation "comprehensive" service when he had actually rendered "brief" or "intermediate" service; and (h) claiming payment for post-operative office visits by surgery patients even though such visits were to be subsumed in the claim for the surgery itself.

Alexander was charged with thirty-one counts of perpetrating this fraudulent scheme by use of the mails, Counts 1-31; eight counts of submitting a false claim to an agency of the United States, Counts 32-39; and one count of making a materially false statement in an application for Medicaid assistance benefits, Count 40. At the close of the Government's case-in-chief, the district court dismissed Count 27, a mail fraud count, on the Government's request. The jury then returned verdicts of guilty on the remaining thirty mail fraud counts, Counts 1-26 and 28-31, five false claim counts, Counts 32-34, 36 and 39, and the single false statement count, that is, Count 40. Alexander moved for a new trial, raising many of the objections now advanced on appeal. Accompanying the new trial motion was a motion for additional discovery, about which more will later be said. The court denied both motions and sentenced Alexander to concurrent thirty-month prison terms and cumulative $500.00 fines on counts 1 and 40, suspended imposition of sentence on the remaining counts, and ordered that the defendant be placed on probation for five years at the expiration of his period of incarceration. This appeal followed.

II

Alexander first argues that the evidence was insufficient to support the jury's verdict of guilty on mail fraud counts 1-4 and false statement counts 32-34 respectively. Because of the dispositive consequences of this contention were it to be upheld, we address it first and, in the end, reject it as to all these counts.

A

Counts 1-4 charged Alexander with use of the mails to defraud CHAMPUS by perpetrating, in violation of 18 U.S.C. § 1341, the eight-part scheme previously outlined. The Government's prosecution of these counts proceeded on two alternative factual theories of guilt: (1) Alexander had fraudulently submitted to CHAMPUS insurance forms which claimed reimbursement for laboratory tests which were not in fact performed and (2) he had submitted claims which falsely indicated that the patient had no other medical insurance.

The record amply supports findings of guilt based on the first, "non-performed tests," theory. Gloria V. Galanda, a CHAMPUS auditor who was one of the Government's principal witnesses, testified that although the CHAMPUS insurance forms submitted by Alexander claimed reimbursement for a number of tests performed for each of the patients involved, his office records failed to indicate any results derived from these tests. Furthermore, the Government's evidence suggested that Alexander's failure to perform tests for which benefits were claimed was a consistent and pervasive pattern in his practice.

A number of Alexander's medical secretaries testified that although they routinely collected and labelled urine specimens, Alexander never tested the samples but directed that they be discarded at the day's end. They also indicated that Alexander rarely reordered supplies. They claimed never to have seen Alexander performing microscopic analysis although he was seen with a slide in his hand on a number of occasions. The only pregnancy test materials seen in Alexander's office by a number of these secretaries were samples from pharmaceutical companies.

Alexander's business records indicated that he routinely tested all of his patients with the same battery of tests. Mrs. Galanda testified to random samples from Alexander's patient records which indicated that in the majority of cases Alexander routinely billed in all cases for urinalysis, wet and dry mount, and smear primary source stain. A substantial number of these billings also claimed reimbursement for pregnancy tests. According to a Blue Cross/Blue Shield "peer-group" analysis prepared and presented in evidence by witness Crumpler, Alexander ranked first among Tidewater-area gynecologists in performing urinalysis, pregnancy and "dry mount" smear tests and second highest for performing "wet mount" tests. Charles Halloran, a Medicaid investigator, compiled and presented in evidence similar peer group data obtaining comparable results.

The combined effect of this evidence, construed in the light most favorable to the Government, sufficed to allow a rational factfinder to find Alexander guilty beyond a reasonable doubt on the "non-performed theory of guilt, Glasser v. United States, 315 U.S. 60, 62 S.Ct. 457, 86 L.Ed. 680 (1942), and we so hold.

B

Whether the evidence also sufficed to support a conviction on the second, "no other insurance," theory is more problematic. For while the evidence undoubtedly supports a finding that in respect of each of the counts under challenge, Alexander submitted insurance forms, falsely disclaiming the existence of "other insurance," it does not as clearly support a finding of the requisite intent to defraud or to obtain "money or property" by means of false statements.

An example illustrates this difficulty. Count 1 alleged that Alexander had submitted to CHAMPUS, on behalf of Margaret Adamson, a claim for $64.00 for services performed on August 1, 1980. This total included claims for an office visit, $50.00, and three tests, billed at $5.00, $5.00 and $4.00 respectively. The claim form indicated that Adamson had no other insurance. In consequence, CHAMPUS paid $48.00 of the claim. Adamson was, in fact, also insured by Blue Cross/Blue Shield, which was "primary" to CHAMPUS in the sense that CHAMPUS required beneficiaries insured by both insurers to exhaust available Blue Cross resources before receiving payments from CHAMPUS. Blue Cross business records indicated, in fact, that Alexander had filed a claim for Adamson's August 1, 1980, visit, but had charged $25.00, $15.00 and $10.00 respectively for the same tests. Blue Cross had allowed $20.00, $10.00 and $6.00 for these tests, leaving unpaid balances of $5.00, $5.00 and $4.00, which were the exact amounts later billed to CHAMPUS. Blue Cross was not billed for the $50.00 office visit fee, but such amounts were not insured under its policy. Whatever the misstatement concerning other insurance then, CHAMPUS was asked only for amounts for which it was primarily liable. Since billing in this manner could not have had the effect of "defrauding" CHAMPUS or of obtaining from it "money" by false representations but would have deprived it only of information, the evidence, it is argued, fails to establish the requisite intent.

We need not, and do not, decide whether that argument has merit. Assuming the evidence is insufficient to support conviction on the second alternative factual theory of guilt, the verdict is nonetheless supportable because of the sufficiency of the evidence on the first. Though under some circumstances a general verdict may so obscure the basis upon which a jury considering alternative theories found guilt that due process will not permit upholding a verdict possibly based upon the unsupported theory, see, e.g., Stromberg v. California, 283 U.S. 359, 51 S.Ct. 532, 75 L.Ed. 1117 (1931); United States v. Head, 641 F.2d 174, 178-79 (4th Cir. 1981), the verdict here may be upheld on the saving principle that by careful record scrutiny it is possible to ascertain with a high degree of probability that the jury here did not rely upon the arguably unsupported theory. See, Turner v. United States, 396 U.S. 398, 90 S.Ct. 642, 24 L.Ed.2d 610 (1970); United States v. Jacobs, 475 F.2d 270 (2d Cir. 1973); see also United States v. Tresvant, 677 F.2d 1018, 1023-24 (4th Cir. 1982) (concurring opinion).

For several reasons, we are satisfied from the record that the jury here relied upon the supported rather than the arguably unsupported factual theory. Most critically, the jury's verdicts on the mail fraud counts, when assessed in relation to the evidence adduced at trial, do not vary depending upon whether the evidence showed that the patients involved did or did not have other insurance not disclosed on Alexander's claim forms. Thus, while the jury convicted on Counts 1-5, 8 and 11, in which the Government's evidence indicated that the patients involved had other insurance contrary to the disclosures on the respective claim forms, it also convicted on Counts 6, 7 and 9, in which the claim forms either made no statement concerning other insurance or correctly indicated that the patient had none.

Additionally, the jury's failure to convict on Counts 37 and 38, is telling. In each of these counts, there was some evidence to suggest that Alexander might have performed the tests, but the evidence of false concealment of other insurance varied. In both counts Alexander's records indicated that a pap smear was performed by an outside laboratory and results were recorded. In Count 37, the Government presented evidence indicating that the claim form falsely denied the existence of other insurance; no such evidence was introduced on Count 38.

We conclude that the record sufficiently indicates that the jury rested verdict on the first, evidentiarily supported theory so that even if the evidence in support of the second were insufficient to support conviction — a question we need not decide — this would not require reversal.

C

The contention that the evidence was insufficient to support conviction on false claim counts 32-34 is without merit. These counts charged false claims by misrepresentation of the existence of other insurance in violation of 18 U.S.C. § 287. The evidence indisputably showed that Alexander misstated the actual fact on each claim; his defense was only that this misrepresentation resulted from carelessness. The jury heard the evidence and simply rejected this theory, concluding instead, as it rationally could, that the misrepresentation was intentionally a false one.

Alexander's further contention that the evidence did not show that the false claims induced payment is misplaced. It need only be proven that they had a "tendency to induce the government to act." United States v. Pruitt, 702 F.2d 152, 155 (8th Cir. 1983). Where, as here, entitlement to payment turned on the non-existence of other insurance, a misrepresentation that this was the fact clearly had the requisite tendency.

D

We therefore hold that the convictions on Counts 1-4 and 32-34 are supported by sufficient evidence under the Glasser standard.

III

We have considered other trial errors assigned by defendant as the basis for reversal or remand for new trial and conclude that none merits relief from the convictions. First, Alexander contends that Count 1 of the indictment fails to charge a critical element of the crime, but we believe that the indictment sufficiently charged Alexander with a fraudulent use of the mails in violation of 18 U.S.C. § 1341. Second, we reject the contention that the indictment as a whole did not give adequate notice of the charges against Alexander; any need for further detail could have been supplied by a timely-requested bill of particulars. The instructions to the jury concerning the credibility of witnesses are, taken as a whole, neither erroneous nor, assuming error, prejudicial. Finally, in connection with defendant's claim of ineffectiveness of counsel, we simply observe that that claim is more properly considered in Alexander's pending motion in the district court for relief under 28 U.S.C. § 2255, and we express no opinion upon it.

IV

Among the grounds for new trial unsuccessfully urged by Alexander in the district court was the Government's alleged failure to produce requested exculpatory material as required by Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) and United States v. Agurs, 427 U.S. 97, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976). The district court's denial of that motion is now assigned as error.

We conclude that the Government's equivocation in making critical factual representations to defense counsel and to the district court concerning its possession of certain of the requested materials fatally compromised the integrity of the proceedings on the new trial motion. In consequence the court's resulting order was tainted and cannot stand on the present record. Because the equivocation was only revealed on this appeal, we have concluded to remand to the district court for reconsideration of the motion in light of the circumstances now revealed and for such further proceedings as may then be indicated. Our reasons are as follows.

Our concern runs to only one of several sets of materials claimed by Alexander to have been withheld in violation of Brady. As to the others, we conclude that the district court did not err in finding no constitutional or statutory violation and that its order denying new trial is not otherwise tainted in respect of those materials. We therefore do not discuss them in detail.

The critical materials are a 1981 Blue Cross/Blue Shield subscriber survey of patients for whom Alexander claimed to have performed services, including most critically patient responses to questions concerning whether services for which Alexander had submitted insurance claims had actually been performed. We summarize the critical developments that have now been revealed respecting these materials, including important events in the process by which the revelation has occurred.

When Alexander made his pre-trial discovery request on May 31, 1983, he knew in general of the existence of the Blue Cross patient survey. Among the materials requested in his motion were all documents "which refer or relate to the claim forms of Blue Cross/Blue Shield. . . ."

At the time this request was received by the Government, the Government had in its possession critical elements of this survey, including the responses of 48 patients for whom Alexander had claimed to have performed services. This is revealed by an investigative agent's case summary earlier prepared in anticipation of possible indictment and prosecution. This summary indicated that the survey results had been turned over to the Government investigators by Blue Cross and, most critically, that thirteen of the forty-eight patients contacted had reported that they did not receive all the services for which Alexander had submitted claims and, by implication, that the remaining thirty-five reported that they had received the services. The summary itself did not reveal the names of the patients in either category, making it impossible to match specific patients surveyed with any specifically identified in the indictment as patients in respect of whom Alexander had made allegedly fraudulent or false claims.

In response to Alexander's discovery request the Government did not produce any materials but instead allowed an open-file discovery by Alexander's trial counsel on June 13, 1983. Whether the patient survey results were in the Government files then made available for inspection is a critical factual question that, for reasons that will appear, is only now revealed to be a fairly disputable, and possibly dispositive, one respecting the claimed Brady violation.

The investigative case summary itself was later turned over to the defense on the eve of trial as Jencks material. As indicated, it would only have revealed that the survey had been made and that its specific results, as summarily reported, were known to the Government and were possibly in its possession in documentary form. The trial was therefore conducted with the Government in possession of the survey results, including the responses of individual patients to the inquiry about services, but with Alexander unaware of those responses, unless they were in the open files made available for inspection, a matter, as indicated, that is now shown to be disputable on the present record.

Following Alexander's conviction, his new counsel sought, incident to a new trial motion, to discover the identity and the specific responses of the forty-eight patients included in the Blue Cross survey. Voluntary disclosure was first sought from the Government and, when that was refused, a motion for discovery was made. The discovery motion was denied and the new trial motion was therefore heard with defense counsel still unaware, as was the district court, of whether any of the patients surveyed were among those identified in specific counts of the indictment and also unaware of the specific responses of any of those surveyed.

It was at this point that the bothersome course of equivocation by the Government began. Before the hearing, the Assistant United States Attorney gave both defense counsel and his own supervisor to understand that the Government's position was that the survey results had not been, and presumably were not then, in the Government's possession. At the oral hearing on the motion, however, the same Government attorney, responding, he later said, to advice given him by Government investigative agents, changed his position and represented to the district court that the materials had indeed been in the Government's possession, but that they were in the Government files opened for defense counsel's pre-trial inspection. On the basis of that advice — which defense counsel plausibly now contends it was unprepared to dispute in view of the Government's prehearing representation — the district court rejected the Brady objection as grounds for a new trial.

Following this unanticipated change of Government position, and with this appeal pending, new defense counsel obtained from Alexander's trial counsel an affidavit stating that he did not recall seeing the survey responses or related audit items in the open file inspection he conducted. On the basis of that affidavit, defense counsel unsuccessfully sought from this court a "partial remand" to the district court to inquire into the facts of the open file inspection, both as incident to reconsideration of its new trial motion and in connection with a 28 U.S.C. § 2255 claim of ineffective assistance of trial counsel. See Part III supra.

When the appeal came on for oral argument in this court, the Government's equivocation on the matter continued. In response to a direct question from this court, the same Government trial counsel flatly represented that the survey materials were, at the critical times, in the possession of Blue Cross and that he had not seen them. This of course reverted to the position represented to defense counsel before the new trial hearing in district court, a position subsequently reversed at that hearing.

This position was once again reversed by Government counsel in response to a court-requested post-argument defense memorandum that appended the investigative case summary showing Government possession of the survey materials by acquisition from Blue Cross. The Government's letter response to this memorandum simply indicated that once again Government counsel had inadvertently misstated the position and that once again Government investigative agents had corrected Government counsel's recollection and recalled for him that the materials were in fact in the Government's possession. This time, however, the Government's position as to whether the materials' were in fact in the open files was itself stated with a new degree of equivocation. Rather than a flat statement that they were in the open files at the time of the inspection, the Government now only asserted that open file discovery was permitted and that, in addition, the Government had "instructed its investigative agents to bring whatever additional materials they had gleaned from Blue Cross."

From this regrettable course of proceedings, we can only conclude that whether the survey materials were actually produced by the open file inspection is a disputable question of fact that, because of the Government's conduct, was not fairly presented as such to the district court. If resolution of that factual question is required to resolve the Brady claim, defendant is now entitled to have it determined by the district court in a hearing appropriate to the factual inquiry.

The question remains, however, whether its resolution is required for that purpose. The Government contends that the defendant has not, in any event, made the requisite showing that the materials were required to be produced under the Brady-Agurs test. The short answer, as defendant points out, is that neither the defendant, nor this court, nor the district court could properly address that question without inspecting the survey responses and related Blue Cross audit materials that the Government now presumably concedes it has had in its possession all along.

It may well be that upon inspection the lack of Brady-Agurs relevance asserted by the Government will readily appear. But the defendant plausibly shows how exculpatory relevance might appear, depending upon the contents of the materials and upon whether the original discovery request specifically or only generally identified these materials. See Agurs, 427 U.S. at 112, 96 S.Ct. at 2401. First, the patient responses — thirty-five of which presumably indicated that services were performed — could tend to rebut the Government's proof of a pervasive practice of not performing tests as a circumstantial means of proving guilt of the specific offenses charged. Second, they could provide credible evidence that Alexander's failure to indicate test results on his office records was not probative that he had not in fact performed them, another facet of the Government's theory of prosecution. Finally, there could be among the thirty-five patients who presumably reported services performed some specifically identified in the indictment as not having received the services claimed.

We of course do not now hold that if any of these possibilities are revealed, they dictate a finding of a Brady violation. That is a judgment for the district court to make based upon the record as a whole. We simply cite them as indicating the defendant's entitlement to disclosure of the survey materials in order properly to press his Brady claim as a basis for new trial if, having inspected them, he concludes so to proceed.

We therefore vacate the district court's order denying new trial, and remand for its reconsideration in accordance with this opinion. Preliminarily, the Government should be ordered by the district court to produce for defendant's inspection all materials in the Government's possession at the time of defendant's pre-trial motion for discovery that related in any way to the Blue Cross patient survey.

If following inspection, the defendant desires to press his motion for new trial on the basis of a Brady violation in respect of those materials alone, he is entitled, upon proper notice to the court and the Government, to have the motion reconsidered on that basis. In that event, the district court should conduct an evidentiary hearing to determine: (a) whether the materials in issue were made available for defendant's inspection in the open file pre-trial inspection permitted by the Government; (b) if not, whether the materials were the subject of specific or general request under Agurs; and (c) on that basis, whether the failure to produce the materials constituted a Brady violation requiring new trial.

Obviously, if the defendant does not timely request reconsideration of his new trial motion, or if the court finds either that the materials in issue were in fact produced by the Government or that failure to produce them did not constitute a Brady violation the motion should be denied as reconsidered.

Except as remanded for the limited purpose of reconsidering defendant's new trial motion, the judgment of conviction is affirmed.

SO ORDERED.