
410 N.W.2d 231 (1987)
STATE of Iowa, Appellee,
v.
Steven Michael ANDERSON, Appellant.
No. 85-1606.
Supreme Court of Iowa.
July 22, 1987.
Rehearing Denied August 19, 1987.
*232 Emmit J. George, Jr., Jeannette M. Keller, and Robert P. Engvall, Iowa City, for appellant.
Thomas J. Miller, Atty. Gen., Christie J. Scase, Asst. Atty. Gen., and Gerald N. Partridge, Co. Atty., for appellee.
Considered by REYNOLDSON, C.J., and HARRIS, LARSON, LAVORATO and NEUMAN, JJ.
LARSON, Justice.
The defendant, Steven Michael Anderson, was charged with assaulting a police officer during an altercation outside a restaurant in Washington, Iowa. Prior to trial, Anderson filed a discovery motion, Iowa R.Crim.P. 13, which requested several items, including "the criminal records of all prosecution witnesses, if any exist...." The trial court ordered the production of all of the materials requested except the criminal records of the witnesses; this part of Anderson's request was denied without elaboration.
Anderson was found guilty of several counts of assault, and he appealed, raising ten issues, including the court's refusal to compel production of the criminal records. He contended the court's refusal to order production of the records violated the disclosure rule of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).
The case was heard by the court of appeals, which ruled, in a four-to-two decision, that the criminal records of the prosecution witnesses may be required to be released if they were available to the State and if they contained evidence admissible at trial which was material to Anderson's case. The court of appeals ordered the case remanded to district court for hearings on those issues but rejected all of the other issues raised. We granted the State's application for further review on the Brady issue and now vacate the court of appeals decision and affirm the judgment of the district court.
Our rules provide for the discovery by the defendant of his own criminal history, or "rap sheet," but not that of the State's witnesses. See Iowa R.Crim.P. 13(2)(a)(3). Anderson argues, however, that production of these records is constitutionally mandated by the familiar Brady rule. The rap sheets were necessary, he claims, to determine if any of the State's witnesses were subject to impeachment. See Iowa R.Evid. 609(a) (conviction of a crime involving dishonesty or false statement as a basis for impeachment).
The State responds that the Brady rule does not mandate production of these records because Anderson has not established a reasonable probability that they would have affected the outcome. See United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383, 87 L.Ed.2d 481, 494 (1985). The State further argues that, under Iowa Code section 68A.7(9) (1983) (now found as Iowa Code section 22.7(9) (1987)), criminal history records such as those sought here are confidential and may not be disclosed unless specifically authorized by Iowa Code section 692.3 (1983). The dissemination requested by Anderson, the State argues, does not fall within the provisions of section 692.3. We first address the Brady argument.

I. The Constitutional Issue.

In Brady, the Supreme Court said that the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or punishment, irrespective of the good faith or bad faith of the prosecution. *233 373 U.S. at 87, 83 S.Ct. at 1196-97, 10 L.Ed.2d at 218 (emphasis added). As we will discuss later, the key to the Brady rule is the word "material."
Brady involved suppression of exculpatory evidence, while in this case Anderson complains of a suppression of impeachment evidence. For purposes of the Brady rule, however, it makes no difference; it applies to both exculpatory and impeachment evidence. See Bagley, 473 U.S. at 676, 105 S.Ct. at 3380, 87 L.Ed.2d at 490; Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104, 108 (1972); 2 C. Wright, Federal Practice § 254, at 74-75 (2d ed. 1982) [hereinafter Wright].
While it has been observed that "disclosure, rather than suppression, of relevant materials ordinarily promotes the proper administration of criminal justice," Dennis v. United States, 384 U.S. 855, 870, 86 S.Ct. 1840, 1849, 16 L.Ed.2d 973, 984 (1966), there is no general constitutional right to discovery in a criminal case, even after Brady. Weatherford v. Bursey, 429 U.S. 545, 559, 97 S.Ct. 837, 845-46, 51 L.Ed.2d 30, 42 (1977); Wright § 254, at 78 n. 48.
In United States v. Agurs, 427 U.S. 97, 103-11, 96 S.Ct. 2392, 2397-401, 49 L.Ed.2d 342, 349-54 (1976), the Supreme Court developed standards for determining materiality under the Brady rule. These standards depended first on the nature of the disclosed evidence, i.e., whether it related to a knowing use of perjured testimony by the prosecution, and second on the specificity of the defendant's request, i.e., whether it was specific or merely one requesting the disclosure of all "Brady material" in general terms. Under Agurs, undisclosed evidence not involving perjury would be material for Brady purposes only if it "might have affected the outcome of the trial." Agurs, 427 U.S. at 104, 96 S.Ct. at 2398, 49 L.Ed.2d at 350. This is the test relied on by Anderson in this case.
The Supreme Court in Bagley, however, abandoned the Agurs test of what "might have affected the outcome" and adopted a test of "reasonable probability." See United States v. O'Dell, 805 F.2d 637, 641 (6th Cir.1986). Under the Bagley rule, undisclosed evidence is material for Brady purposes only if the defendant shows a reasonable probability that, if the evidence had been produced, the outcome would have been different. Bagley, 473 U.S. at 682, 105 S.Ct. at 3384, 87 L.Ed.2d at 494.[1]
In Bagley, the government's only two witnesses had signed agreements to furnish information and testimony for a fee. Prior to trial, the defendant filed a motion for disclosure of "any deals, promises or inducements made to witnesses in exchange for their testimony." The government's response did not reveal the fact its witnesses had a financial interest in the case. The government further obscured the picture of the witnesses' interest in the case by its response to the defendant's request for "[c]opies of all Jencks Act material." Its response included an affidavit by each of the key witnesses which stated, "I make this statement freely and voluntarily without any threat or rewards, or promises of reward having been made to me in return for it."
Bagley argued that the failure of the government to respond to his request for production of the fee agreements and the *234 misleading statement in the affidavits resulted in a denial of due process under the Brady rule. In addressing this claim, the Court in Bagley adopted the test paralleling that for effective assistance of counsel announced in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984): "When a defendant challenges a conviction, the question is whether there is a reasonable probability that, absent the errors, the fact finder would have had a reasonable doubt respecting guilt." Strickland, 466 U.S. at 695, 104 S.Ct. at 2068-69, 80 L.Ed.2d at 698. The Court in Bagley stated:
We find the Strickland formulation of the Agurs test for materiality sufficiently flexible to cover the "no request," "general request," and "specific request" cases of prosecutorial failure to disclose evidence favorable to the accused: The evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A "reasonable probability" is a probability sufficient to undermine confidence in the outcome.
473 U.S. at 682, 105 S.Ct. at 3384, 87 L.Ed.2d at 494.
What evidence presented by Anderson points to a reasonable probability that the undisclosed rap sheets would have resulted in a different outcome of the trial? As Bagley itself notes, a "reasonable" probability must be so substantial that it undermines confidence in the outcome of the case. 473 U.S. at 682, 105 S.Ct. at 3384, 87 L.Ed.2d at 494.
The burden of proof is on a defendant claiming a Brady violation to establish materiality. See United States v. Boschetti, 794 F.2d 416, 418 (8th Cir.1986); cf. Wright § 254, at 66-67 (showing under federal evidence rules).
We recognize that it is difficult for a defendant who has been denied access to the materials to establish with specificity what effect they might have had on his trial. As one writer has said,
[o]ne can't imagine the baffling problems of particularizing a need or interest when the party has no access to the evidence he seeks to discover. How does Tantalus particularize that which is out of his sight as well as his reach?
Traynor, Ground Lost and Found in Criminal Discovery, 39 N.Y.U. L. Rev. 228, 230 (1964).
Nevertheless, it is incumbent upon the defendant to make a threshold showing of how the withheld evidence would have affected his case. In the trial court, when Anderson requested the rap sheets of the witnesses, he gave no reasons for his request. He now contends, and we assume, that the reason he wanted them was for possible use for impeachment, that one or more of the potential witnesses might have had a conviction record. Apparently, Anderson made no inquiry about prior convictions of the witnesses, either in their pretrial depositions or in their cross-examination at trial. On appeal, he merely contends that, if the witnesses had such convictions in their backgrounds, the result of his trial might have been different.
A similar argument was made in United States v. Peltier, 800 F.2d 772 (8th Cir. 1986), in which the government had withheld evidence which the defendant claimed might have aided him in the cross-examination of the government's witness. The Court said:
There is a possibility that the jury would have acquitted Leonard Peltier had the records and data improperly withheld from the defense been available to him in order to better exploit and reinforce the inconsistencies casting strong doubts upon the government's case. Yet, we are bound by the Bagley test requiring that we be convinced, from a review of the entire record, that had the data and records withheld been made available, the jury probably would have reached a different result. We have not been so convinced.
800 F.2d at 779-80. Accord United States v. Cadet, 727 F.2d 1453, 1465-66 (9th Cir. 1984) (showing of materiality not satisfied by mere conclusory allegations).
When an assertion of materiality is made in support of a Brady argument, a *235 reviewing court should itself consider any adverse effect that the failure to disclose might have had on the preparation or presentation of the defendant's case in light of the totality of the circumstances. Bagley, 473 U.S. at 682, 105 S.Ct. at 3384, 87 L.Ed.2d at 494.
Simply alleging, as Anderson has, that he might have found impeaching evidence in the rap sheets and, if so, that it might have aided his defense, does not establish a threshold case of materiality sufficient to justify a remand for a hearing in district court as the court of appeals did in the present case. See Boschetti, 794 F.2d at 418; United States v. Auten, 632 F.2d 478, 480 (5th Cir.1980) (mere conclusory assertions that government used perjured testimony not sufficient to require evidentiary hearing); cf. Wright § 254, at 66-67 (discovery under federal evidence rule).
Even if we were to assume that one or more of the State's witnesses had had a prior conviction, that fact standing alone would not rise to the level of a reasonable probability of a different result. Peltier, 800 F.2d at 779. In this case, three police officers, the manager of the restaurant where the assault occurred, one of the employees of the restaurant, and another eyewitness all testified to substantially the same facts. Actually, Anderson did not seriously challenge that testimony; his defense was that he struck the officers to protect a friend who was involved in a scuffle with one of them. Under these circumstances, it cannot be seriously argued that witness credibility was the "slender reed" on which the State's case rested. See United States v. McCrane, 547 F.2d 204, 206 (3d Cir.1976).
In light of the totality of the circumstances, Anderson has not shown that there is a reasonable probability that the outcome would have been different. Because Anderson failed to establish a threshold showing of materiality, we reject his constitutional claim.
II. The Confidentiality Issue.
Great solicitude has been shown by our statutes and cases for the privacy of the persons who are the subjects of criminal history records. Under Iowa Code section 68A.7(9) (1983) (now found as Iowa Code Section 22.7(9) (1987)), criminal history records, such as those sought here, are confidential. They may not be disclosed unless authorized by Iowa Code section 692.3, Feeney v. Scott County, 290 N.W.2d 885, 887-88 (Iowa 1980), and a dissemination such as requested by Anderson is not authorized by that section.
In a related case, we held that disclosure may be ordered "only when there is a reasonable basis for believing that the rap sheet may contain information that is pertinent to the individual's selection as a juror and that is unlikely to be discovered through voir dire or through juror questionnaires." State v. Bessenecker, 404 N.W.2d 134, 138 (Iowa 1987). We further noted in Bessenecker that
the legislature has set a tone of caution against the dissemination of criminal history data except as specified. The legislature restricted the distribution of such data to an exclusive group of agencies and departments, and then provided for its release only under specified conditions.
404 N.W.2d at 137.
Anderson's disclosure request was not even limited to a list of convictions; it asked for the whole record, which would include other, inadmissible evidence. In this regard, it has been said that
[s]ince it is not ordinarily permissible in most jurisdictions to show that a witness has been arrested, or charged with or prosecuted for a criminal offense, or confined in jail or prison, or to inquire about those facts on cross-examination, where no conviction is shown, for the purpose of impairing his credibility, it is not surprising that the courts have usually, although not always, viewed with disfavor attempts by defendants to obtain disclosure of such records about prosecution witnesses. Similarly, in the few cases involving probation or parole records of prosecution witnesses, the courts have denied, or upheld the denial *236 of, defense motions seeking disclosure thereof.
Annotation, Accused's Right to Discovery or Inspection of "Rap Sheets" or Similar Police Records About Prosecution Witnesses, 95 A.L.R.3d 832, 838 (1979) (footnotes omitted).
We conclude that the due process claim asserted here must fail and further that the disclosure of the materials requested is prohibited by our confidentiality statutes. We therefore vacate the court of appeals decision and affirm the judgment of the district court.
DECISION OF COURT OF APPEALS VACATED; DISTRICT COURT JUDGMENT AFFIRMED.
NOTES
[1]  It should be noted that the portion of the Bagley opinion establishing the "reasonable probability" standard, authored by Justice Blackmun, was joined only by Justice O'Connor. The concurring opinion by Justice White, and joined by Chief Justice Burger and Justice Rehnquist, however, approved the "reasonable probability" standard of the Blackmun opinion. 473 U.S. at 685, 105 S.Ct. at 3385, 87 L.Ed.2d at 496. When there is no clear majority, we look to the positions taken by those members who concurred in the judgment on the narrowest ground. See United States v. Severdija, 790 F.2d 1556, 1560 n. 2 (11th Cir.1986).

The majority of federal appellate courts have interpreted Bagley as establishing a reasonable probability standard. See, e.g., United States v. Brimberry, 803 F.2d 908, 914 (7th Cir.1986); Reese v. Fry, 801 F.2d 348, 351 (8th Cir.1986); Severdija, 790 F.2d at 1560; United States v. Kelly, 790 F.2d 130, 136 (D.C.Cir.1986); United States v. Ben M. Hogan Co., 769 F.2d 1293, 1299 (8th Cir.1985); Lindsey v. King, 769 F.2d 1034, 1041 (5th Cir.1985); United States ex rel. Smith v. Fairman, 769 F.2d 386, 393 (7th Cir.1985).
