JAMES DICKSON PHILLIPS, Circuit Judge:

Dr. Peter V. Alexander appeals from the district court’s denial of his motions for a new trial and for relief under 28 U.S.C. § 2255. The district court concluded that alleged failures by the government to supply material to Alexander prior to trial did not warrant a new trial, and that Alexander had not shown deficiencies in the indictment or ineffective assistance of counsel that would permit relief under § 2255. We affirm.

Dr. Alexander, who operated a medical practice in Virginia Beach, Virginia, was convicted in 1983 of multiple counts of mail fraud, the submission of false claims, and the making of materially false statements in connection with the submission of medical insurance claims. On direct appeal, this court affirmed the conviction in most respects, but remanded the case to the district court for consideration of Alexander’s motion for a new trial on the grounds of failure by the Government to produce Brady materials. United States v. Alexander, 748 F.2d 185 (4th Cir.1984) (Alexander I).

The indictment of Alexander alleged that between 1978 and 1982, he perpetrated a fraudulent scheme in his dealing with three health insurers: Medicaid, Blue Cross/Blue Shield, and the Civilian Health and Medical Program of the Uniform Services (CHAM-PUS). The fraud included submitting duplicate claims to more than one insurer, submitting false claims to all three, falsely claiming that unperformed services had been performed, claiming to perform pregnancy tests on sterilized women, claiming higher fees from insured patients than from non-insured patients, falsely claiming to have diagnosed illnesses during routine office visits in order to receive compensation from CHAMPUS and Medicaid, falsely claiming to have rendered comprehensive services, and claiming reimbursement for post-operative office visits already claimed under the surgery claim itself.

Alexander was indicted on numerous counts of mail fraud, submitting false claims, and making false statements in furtherance of the fraudulent practices. After a jury trial, he was convicted of most of the counts in the indictment. He then sought a new trial on numerous grounds, including the alleged failure to supply as Brady material a Blue Cross survey of patients for whom Alexander claimed to have provided services. Alexander also moved for relief under 28 U.S.C. § 2255 (1982), claiming that the indictment was invalid and that he had received ineffective assistance of trial counsel. After this court ordered the district court to conduct an evidentiary hearing on the Brady question, Alexander was permitted to conduct additional discovery. He subsequently filed new motions for a new trial, alleging newly discovered evidence that the government had failed to produce other materials required to be produced under Brady, the Jencks Act, 18 U.S.C. § 3500 (1982), and Rule 16 of the Federal Rules of Criminal Procedure. He claimed in particular that prior to trial the government should have produced grand jury testimony, government prosecutor reports and case files, CHAMPUS, Blue Cross and Medicaid audit work papers, patient, expert and employee *1048 interviews and notes, notes of an undercover agent, computer tapes, printouts, and parameters for Medicaid and Blue Cross peer group analyses, and CHAMPUS audit protocol rules.

The district court found that Alexander had received the Blue Cross patient survey that prompted our remand in Alexander I. The court also concluded that the attorneys who represented Alexander at trial had not provided ineffective assistance of counsel. The court held that Alexander waived any right to object to the indictment by failing to move for its dismissal before trial, and that Alexander cannot properly challenge the competency and inadequacy of the evidence before the grand jury. The court also rejected each of Alexander’s new Brady, Jencks Act, and Rule 16 claims. This appeal followed.

Alexander first argues that the grand jury minutes and testimony, which he did not receive before trial, indicate that the grand jury did not hear competent evidence on the charges contained in the indictment. The district court found that Alexander waived his opportunity to challenge the indictment by failing to object prior to trial, as required by Fed.R.Crim.P. 12(f), but also proceeded to consider and reject Alexander’s substantive attack on the indictment. We conclude that Alexander’s challenges to the indictment may be disposed of without resolving whether the government’s failure to produce grand jury material violated a duty in it to do so, and also find that Alexander can now properly make the challenges to the indictment urged on this appeal.

In Alexander I, we considered and rejected Alexander’s contention that the indictment as a whole did not give adequate notice of the charges against him. 748 F.2d at 190. On this appeal, Alexander asks that we look behind the indictment to determine whether the grand jury heard competent and specific evidence on the charges made. He argues that the government’s primary grand jury witness, Michael Powell, a government criminal investigator, presented unsubstantiated and hearsay testimony to the grand jury, and that, in any case, the evidence before the grand jury was not sufficiently specific as to support the allegations of the indictment.

In Costello v. United States, 350 U.S. 359, 76 S.Ct. 406, 100 L.Ed. 397 (1956), the Supreme Court rejected the claim that an indictment might be found invalid if it was based wholly on hearsay grand jury testimony. The court noted the traditional independence of grand juries, and concluded that “[a]n indictment returned by a legally constituted and unbiased grand jury ... if valid on its face, is enough to call for a trial of the charge on the merits.” Id. at 363, 76 S.Ct. at 408.

Despite the clear import of Costello, Alexander calls our attention to several lines of authority that he asserts enable this court to find that the district court should have dismissed the indictment. Each of these cases may be distinguished. First, many of the cases address whether an indictment is facially valid. See, e.g., United States v. Cecil, 608 F.2d 1294 (9th Cir. 1979); United States v. Nance, 533 F.2d 699 (D.C.Cir.1976). We addressed and rejected Alexander’s claim of facial invalidity in Alexander I. Second, a number of cases that Alexander relies upon draw on Justice Burton’s separate concurring opinion in Costello, where he indicated that an indictment without a basis in grand jury evidence should be subject to dismissal. Costello, 350 U.S. at 364-65, 76 S.Ct. at 409 (Burton, J., concurring). See, e.g., United States v. Romero, 585 F.2d 391, 399 (9th Cir.1978). While Justice Burton’s view would indeed permit some latitude in piercing the allegations that appear on the face of an indictment, it has never commanded another vote in the Supreme Court, and fails to overcome the clear command of the majority in Costello that a facially valid indictment suffices to permit the trial of the party indicted.

Finally, Alexander points to Russell v. United States, 369 U.S. 749, 82 S.Ct. *1049 1038, 8 L.Ed.2d 240 (1962), for the proposition that the apparent rule in Costello was later relaxed by the court. In Russell, defendants were indicted for failing to answer questions put to them by a congressional committee. The indictment failed to specify the questions not answered, and the court held that such unspecificity could not be cured by a bill of particulars. A bill of particulars would permit the government to prosecute for an act that was not the basis for the grand jury’s indictment. In this case, by contrast, the indictment of Alexander specified numerous fraudulent acts arising out of large multi-claim reimbursements by various insurers to Alexander. The claims for which Alexander was convicted were a subset of those charged in the indictment, and not potentially separate crimes, as in Russell. Russell therefore fails to support Alexander’s challenge to the indictment. Because the indictment was valid on its face, Alexander was properly brought to trial for the charges of which he was eventually convicted.

Ill

Alexander next argues that the government’s failure to produce a number of documents before trial violated the government’s obligation under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), the Jencks Act, 18 U.S.C. § 3500 (1982), and Rule 16 of the Federal Rules of Criminal Procedure. Because Alexander’s claims here relate to a number of types of documents, we analyze separately his claims as to these materials.

First, Alexander contends that the government should have produced the computer printouts and programs used to complete “peer-group” analyses prepared and presented at trial by Medicaid and Blue Cross investigators. The two peer group studies show that Alexander ranked very high, among the groups of physicians studied, in the number of laboratory tests billed to the insurers. 1 Alexander asks us to find that the failure to provide him with the computer data and programs relied upon for the peer group studies prevented his trial attorneys from conducting adequate cross-examination, in violation of the confrontation clause of the sixth amendment, and that the information withheld might have affected the outcome of his trial.

Alexander’s trial attorneys might have challenged the peer-group testimony at trial by objecting to its character as computer study evidence and thereby requiring the government to introduce the underlying data and programs as a foundation for the study results, but failed to do so. The Blue Cross computer printouts merely listed for each medical provider the percentage of the provider’s patients for whom Blue Cross had been billed for a particular service, and the Medicaid printouts similarly involved comparisons of Alexander’s billings per patient with averages for a comparable peer group. Given a timely challenge, the government could have attempted to show the reliability of the computer studies, see United States v. Russo, 480 F.2d 1228, 1239-40 (6th Cir.1973). Alexander thus waived his confrontation clause argument by failing to raise it at trial. See United States v. Fendley, 522 F.2d 181, 184-87 (5th Cir.1975).

The Jencks Act, which requires the production of statements of testifying government witnesses, does not apply to the peer programs and printouts, and Alexander’s challenge on this basis fails. See United States v. Dioguardi, 428 F.2d 1033, 1037-38 (2d Cir.1970). Alexander’s Rule 16 claim was waived by his failure to specifically request production of the computer materials before trial. See Russo, 480 F.2d at 1241-43.

To make out a Brady violation, Alexander is obliged to show that the undisclosed evidence “creates a reasonable *1050 doubt that did not otherwise exist” as to his guilt. United States v. Agurs, 427 U.S. 97, 112, 96 S.Ct. 2392, 2401, 49 L.Ed.2d 342 (1976); United States v. Bagley, — U.S. -,-, 105 S.Ct. 3375, 3385, 87 L.Ed.2d 481 (1985). A failure to demonstrate a possible effect on the trial outcome makes the government’s failure to produce evidence harmless. Chavis v. North Carolina, 637 F.2d 213, 223 (4th Cir.1980).

Some constructions of the peer group data place Alexander in a somewhat more favorable light than the analyses testified to at trial. Alexander argues that the computer material is therefore exculpatory, and would have been material to the jury’s evaluations on intent. We find, however, that the nonproduction of the computer material did not potentially affect the outcome of the trial. The government presented evidence that Alexander lacked the equipment and supplies to perform the tests for which he billed the insurers, and that his files reflected fraudulent practices. Alexander’s files showed that insurers were billed for pregnancy tests on a woman who had been sterilized. Alexander explained his lack of a microscope capable of performing the tests for which he billed by testifying that his real microscope had been sent to- Romania for repair and that the Romanian mails were notoriously slow. His own employees testified that they never saw Alexander perform most of the tests for which he billed, and that they were instructed to throw out test samples at the end of working days. Patient records did not document results for the tests for which insurers were billed. Given this wealth of evidence on Alexander’s fraudulent intent, we cannot say that there is a reasonable possibility that the pretrial production of Medicaid and Blue Cross computer data would have created the requisite doubt as to his guilt.

Second, Alexander claims that he did not receive before trial the audit notes and work papers from the CHAMPUS, Blue Cross, and Medicaid audits of his billings, and was not afforded the opportunity to examine the audit protocol for the CHAMPUS audit. Alexander contends that he was prejudiced by the failure to receive access to these materials before trial because the audit notes would have rebutted the government’s theory that Alexander fraudulently indicated that some patients had no other insurance, while Alexander was actually billing two insurance companies, and that the CHAMPUS audit protocol held Alexander to accounting standards not required by law.

Again, we are unable to find that the government’s failure to produce these audit materials amounted to a Brady violation. In Alexander I, we found specifically that we did not need to reach the issue whether the evidence was sufficient to convict Alexander on the government’s “no other insurance” theory because the jury relied upon the government’s theory of actual fraud. 748 F.2d at 189-90. Thus, any alleged Brady violation that affects the no other insurance theory was harmless. The CHAMPUS protocol, which imposed an auditing convention requiring a separate lab report for each test procedure performed, conceivably created an obligation that was not required by law. Nevertheless, this argument was developed by Alexander’s counsel at trial, and the failure to produce the protocol did not constitute a Brady violation. 2

Alexander also asserts that the government failed to produce or destroyed notes of interviews with some of Alexander's Medicaid patients, and that the government should have produced notes *1051 relating to an undercover visit by an agent who posed as a patient. Some of the Medicaid interviews indicated that Alexander had taken the samples necessary to perform the tests for which he later billed Medicaid, and Alexander asserts that this material is exculpatory because it shows that the tests were performed. Alexander billed Medicaid for several tests he claimed to have performed on the Medicaid agent, Stehm, even though Stehm testified that she never left, for example, a urine sample that would have been necessary to perform the urinalysis for which Medicaid was billed. Alexander argues that the government should have produced evidence that Stehm was instructed not to leave a urine sample, a fact that would have indicated that she departed from the usual office procedure and that the billing for the urinalysis was a mistake.

Once more, Alexander fails to demonstrate that a Brady violation occurred. The interviews with Medicaid patients would have shown, at most, that the patients were aware that they had given urine and other samples needed for tests to be performed. The patients would themselves have had no knowledge of whether the tests were actually performed, and indeed, additional evidence that samples were taken might have buttressed the government’s theory that it was Alexander’s practice to collect samples and throw them away without testing. Evidence that Stehm was instructed not to leave a urine sample would only have highlighted and given more credibility to Stehm’s testimony that Alexander could not have performed the test for which Medicaid was billed. Given the other evidence of testing practices by Alexander, the government’s failure to produce Stehm’s written notes or instructions did not constitute a material violation of Brady.

Finally, we examine Alexander’s assertion that he was denied the effective assistance of trial counsel. Under the test of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), Alexander must show that the performance of his trial attorneys was deficient, and that he was so prejudiced by their inadequacy that there is a reasonable probability that the result of his trial would have been different, but for the specific ineffectiveness proven.

The deficiencies in counsels’ performance at trial asserted by Alexander on appeal relate to the two Brady claims just examined. Alexander argues that his attorneys should have utilized the evidence that Medicaid patients had indicated that samples were taken from them, and should have emphasized that Stehm’s failure to leave a urine sample was a premeditated effort to circumvent office procedure that could not have been anticipated by Alexander. As we observe below, the full use of this evidence at trial would not have given rise to a reasonable probability that the outcome of Alexander’s trial would have been different. Moreover, we observe that Alexander also fails to show that his attorneys’ performance, in any case, fell below the standards for effective assistance of counsel. His attorneys made a strategic choice not to engage in a paper chase. Alexander was a poor recordkeeper, and an attempt to specifically challenge the government’s allegations that specific patients were not actually tested would have emphasized the number of patients for which Alexander could not produce test results. Alexander’s attorneys made a strategic choice to rely on a credibility defense, and the district court found as a fact that Alexander was informed of and agreed with this strategic decision. Under Strickland, we are not permitted to second-guess the strategic decisions of Alexander’s attorneys, 466 U.S. at 681, 104 S.Ct. at 2061, and we therefore find that Alexander has not shown ineffective assistance under either prong of the Strickland test.

We have examined the other errors assigned by Alexander as the basis for a new trial or § 2255 relief and conclude that *1052 none merits relief from his convictions. The judgment of the district court is affirmed.

AFFIRMED.

Notes

. In Alexander I, we held that the admission of these studies by the district court was not an abuse of discretion. 748 F.2d at 188 n. 6.

. In fact, the district court found that the audit reports were turned over to Alexander before trial, and the government suggests that the CHAMPUS audit report detailed the protocol criteria. We need not reach the question whether the record supports the finding that these materials were actually produced, however, because we conclude that in any case, their non-production did not violate Brady.