
658 F.3d 772 (2011)
Jamie J. JARDINE, Petitioner-Appellant,
v.
Mike DITTMANN, Respondent-Appellee.
No. 09-3929.
United States Court of Appeals, Seventh Circuit.
Argued June 14, 2011.
Decided September 14, 2011.
Rehearing En Banc Denied October 14, 2011.
*773 Robert J. Palmer, Attorney, May, Oberfell & Lorber, Bryan Mackenzie, Law Student, Mishawaka, IN, for Petitioner-Appellant.
Warren D. Weinstein (argued), Assistant Attorney General, Office of the Attorney General, Wisconsin Department of Justice, Madison, WI, for Respondent-Appellee.
Before POSNER, ROVNER, and WOOD, Circuit Judges.
PER CURIAM.
Jamie Jardine, imprisoned in Wisconsin for sexual assault and attempted homicide, appeals the dismissal of his petition for a writ of habeas corpus. See 28 U.S.C. § 2254. Although the district court dismissed the petition summarily, it granted Jardine a certificate of appealability to pursue his claim that, at trial, Wisconsin officials withheld from him material, exculpatory evidence in violation of his Due Process rights. See Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We affirm. In doing so, we acknowledge that Jardine's criminal case featured police misconduct. But this appeal illustrates how the constitutional rule announced in Brady does not reach every instance of misconduct. Brady covers only material evidence, and in Jardine's case the materiality prong has real bite. At bottom, Jardine was doomed by his own testimony, and that fact prevents us from concluding that the state court was unreasonable in finding the missing evidence immaterial.

I.
In 1994, a Wisconsin jury convicted Jardine of sexually assaulting and attempting *774 to kill Laurie Grandhagen, a masseuse at Kady's Sauna and Massage Parlor in Superior. He was sentenced to 60 years' imprisonment. State-court opinions and the petition show that Grandhagen and Jardine told two very different stories at trial.
According to Grandhagen, Jardine got violent after a massage. He brandished a gun, handcuffed and sexually assaulted her, then asked about the parlor's money stash and led her down a hall at gunpoint. Before finding any money, however, he removed the handcuffs and forced Grandhagen to her knees. Fearing for her life, Grandhagen lunged for Jardine's gun when he displayed it a second time. From there her memory is blank, but the ensuing struggle left her with a crushed skull and a gunshot wound in her thigh. To explain the skull fracture and attendant brain trauma, a doctor testified that the features of the wound were consistent with pistol-whipping with the butt of a gun like Jardine's. The record does not reveal whether Jardine took any money.
Jardine's story had similar elements but a different bent. He testified that he usually carried a pistol and handcuffs for his work as a security guard, and that he had been driving around with the gun that day, contemplating suicide; he changed his mind and went for a massage instead. Jardine, a repeat customer at Kady's, had previously paid another masseuse there (not Grandhagen) for sexual favors in addition to run-of-the-mill massages. During this session, he inadvertently revealed his gun to Grandhagen, who then volunteered that the two could have sex; Jardine, confused, acquiesced. But he needed extra help getting aroused, so he and Grandhagen agreed to use the handcuffs; after sex, he removed them at her request, without ever seeking the parlor's money stash or holding her at gunpoint. And although Jardine admitted asking Grandhagen to kneel after having sex, he testified that he did so for "no real reason." He then showed his gun to Grandhagen again, this time to demonstrate that it was harmless in his hands. But the demonstration went awry: Grandhagen inexplicably seized the gun, which went off, sending her to the floor. Jardine, seeing blood on Grandhagen's head and assuming that she had been shot there rather than her leg, panicked and fled. When police first questioned him, he denied that he had been at the massage parlor that night, but he later admitted he had been there. At no time could he explain how Grandhagen's head was injured.
Jardine was convicted, and he combined his direct appeal with an unsuccessful motion for a new trial based on a letter from another masseuse who somehow contradicted both Grandhagen's trial testimony and his. After Jardine lost on appeal, he petitioned the Supreme Court of Wisconsin for review. And while his petition was pending, the trial court received a new letter from a police detective who admitted doctoring the crime scene in some manner to hide evidence of prostitution at Kady's.
On the basis of the detective's letter, Jardine filed another new-trial motion, which the trial court ignored for years. Eventually, Jardine renewed his motion; the trial court cursorily dismissed it; and, later, the Court of Appeals remanded the case to the trial court for further consideration, "because the real controversy regarding the letter allegedly from the detective ha[d] not been heard." Further, the court explained, the allegations went "to the crux of the State's case" and seemed "particularly relevant to the sexual assault charges and are too important to be left unresolved." Yet, while the motion was again pending in the trial court, Jardine's counsel withdrew it; the record does *775 not show precisely when. And lateragain, the record does not say whenJardine filed a new motion for DNA testing and related relief. His motion was granted, at least with respect to the DNA testing. Among the items tested were semen-stained sheets and towels from the massage parlor, apparently withheld by the detective in the run-up to trial, and Jardine's gun. At least three other men (and not Jardine) had ejaculated on the sheets and towels at some time, and the butt of the gun yielded no testable genetic material.
The trial court denied Jardine any relief on the basis of the test results, however, and the Court of Appeals upheld that determination in a written, unpublished decision. The Supreme Court of Wisconsin denied review.
Jardine then filed a petition under 28 U.S.C. § 2254, arguing, as relevant here, that the sheets and towels, together with the gun, were unconstitutionally suppressed before and at trial. The district court summarily dismissed the petition without requesting a response from the warden or additional state-court records, concluding that Jardine's claim about the DNA-tested evidence failed on the merits and any other claims were untimely. Days later, Jardine requested a certificate of appealability, which the district court granted. He moved simultaneously for reconsideration, and the district court ordered that motion administratively terminated.

II.
Jardine argues that his gun and the stained sheets and towels from the massage parlor were exculpatory, material evidence suppressed by Wisconsin officials in violation of his Due Process rights as outlined in Brady. (The certificate of appealability suggested that Jardine could also argue ineffective assistance of counsel, but his briefs are silent on that issue.) The warden attacks the materiality of the evidence, but first questions whether the petition is timelyalthough he concedes that gaps in the record left the district court unable to answer that question. The warden also asserts that Jardine defaulted his claims by failing to apprise the Wisconsin courts of their federal nature. Jardine's state-court filings are mostly absent from the record, and their absence clouds any inquiry into timeliness or default. Because we can resolve the merits but not the procedural questions on the scant record, we turn directly to the substance of Jardine's claims.[1]


*776 A.
The parties dispute the exculpatory value of Jardine's gun, the butt of whichyears after trialcontained no trace of Grandhagen's DNA. Jardine says this shows his gun was not used to bash her head in; the warden says otherwise, trading on the time Jardine had to wipe away any gore before he was caught. But in this fight the parties overlook a simpler problem: by Jardine's account, Wisconsin never suppressed the gun. Suppression, for Brady purposes, happens only when prosecutors and police fail to disclose evidence not otherwise available to a reasonably diligent defendant. United States v. Gray, 648 F.3d 562, 566-67 (7th Cir.2011); Harris v. Kuba, 486 F.3d 1010, 1015 (7th Cir.2007). Nothing in Jardine's petition suggests his defense team was unaware of his own gun's existence, the state's possession of it, or the prosecution's theory of its role in the crime. Nor does Jardine allege that he unsuccessfully requested access to the gun. Thus, Jardine's Brady claim about his gun never leaves the ground. See Harris, 486 F.3d at 1015 (prosecution did not withhold defendant's own alibi from him); United States v. Lee, 399 F.3d 864, 865 (7th Cir.2005) (prosecution did not suppress defendant's own pants, which contained a gun).[2]

B.
At first blush, Jardine's argument about the semen-stained sheets and towels, which showed (after DNA testing) that other men had sexual encounters at the parlor, gets more traction. (Jardine also mentions a hair sample that turned out not to be his, but the hair could easily belong to the purchaser of a bona fide massage.) The evidence supports his contention that the parlor doubled as a brothel and, according to him, explains why Grandhagen might have offered him sex, reveals her motivation to cover up her prostitution career by lying, and contradicts the testimony of Denise McKay, another masseuse who denied generally that prostitution took place at the parlor and specifically that Jardine had once purchased her sexual services. Derivatively, Jardine argues that the evidence of prostitution could, by bolstering his testimony that Grandhagen consented, negate his motive to fatally silence a rape victim. What is more, the evidence seems to have actually been suppressed.
But not all suppressed evidence that has some tendency to exculpate or impeach is material under Brady, and relief may be granted only if introducing the evidence would have cast "the whole case in such a different light as to undermine *777 confidence in the verdict." Strickler v. Greene, 527 U.S. 263, 290, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (quoting Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)). Logically, inadmissible evidence is immaterial under this rule. Moreover, because this proceeding is subject to 28 U.S.C. § 2254(d), Jardine can prevail only if he shows that the state court's materiality determination was unreasonable, rather than merely incorrect. See Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 785-86, 178 L.Ed.2d 624 (2011). This court must fill any gaps in the state court's discussion by asking what theories "could have supported" the state court's conclusion. Id. at 786.
Here, Jardine's argument that the evidence of prostitution was material founders on his own testimony. His story places him alone at the scene and raises a very troubling question: How was Grandhagen's head injured so badly on the night she was shot in the leg, and in a manner that suggested pistol-whipping with the butt of a gun like Jardine's? Even if we imagine, for the sake of argument, that the blood Jardine says he saw on Grandhagen's head had spurted to that location from the gunshot wound in her leg, how likely is it that some other malefactor with a similar gun appeared on the scene that same night and took the opportunity to pistol-whip her? Or is Jardine's theory that when he shot her (inadvertently, by his account), her fall caused an injury that a medical expert would mistake for a pistol-whipping wound? Most important, would knowing that one or more of the masseuses (maybe Grandhagen, maybe not) was a prostitute help a reasonable juror answer either of these questions in Jardine's favor? We think not. There is no room in Jardine's own story for other attackers, notwithstanding Grandhagen's initial confusion, in early police interviews, about how many attackers there were, or her misidentification of Jardine in a photo line-up some time during or after her recovery. Nor is there a plausible basis for contending that the evidence of prostitution somehow means Grandhagen suffered a freakish fall, rather than the pistol-whipping suggested by expert analysis of her injuries.
Jardine faces still another obstacle to collateral relief: A Wisconsin court already concluded that the evidence of other men's fluids on sheets and towels would be inadmissible under state law. If used to show that Grandhagen herself had sex with other customers, either to bolster Jardine's testimony that she consented or to impeach her generally, introducing the evidence would violate Wisconsin's sweeping rape-shield law, Wis. STAT. § 972.11(2). If used to impeach McKay, the witness who denied trading sex acts for Jardine's money and testified that there was no prostitution at the parlor, it apparently would fall afoul of the state's rule against impeachment through extrinsic evidence of collateral acts, Wis. STAT. § 906.08(2). So the state court concluded, and federal courts in § 2254 proceedings defer to state-court descriptions of state law even if they do not agree with those descriptions. Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991); Sussman v. Jenkins, 636 F.3d 329, 352 (7th Cir.2011); George v. Smith, 586 F.3d 479, 484 (7th Cir.2009), cert. denied, ___ U.S. ___, 130 S.Ct. 3414, 177 L.Ed.2d 327 (2010). Furthermore, the Wisconsin court did not see, and Jardine has not explained, how evidence that prostitution took place at Kady's could be relevant if not used to support inferences about Grandhagen's own sexual activity or to impeach McKay.
Still, the evidence would be material for Brady purposes if, had the defense known of that evidence and sought to introduce it at trial, the state rules would necessarily have yielded to Jardine's federal rights *778 under the Confrontation Clause. Cf. Sussman, 636 F.3d at 352, 358 (explaining, in ineffective-assistance context, that petitioner can show prejudice if Wisconsin court's determination of inadmissibility under rape-shield law would itself violate Confrontation Clause). In light of § 2254(d) and Harrington, see 131 S.Ct. at 785-86, the relevant question is whether a reasonable court would have been forced to deem the evidence of prostitution "highly probative, noncumulative, nonconfusing, nonprejudicial ... [and] vital to the central issue in the case," Redmond v. Kingston, 240 F.3d 590, 592 (7th Cir.2001). But evidence that a sexual-assault complainant often consented to sex with other men is archetypally prejudicial and not highly probative of consent in a particular case; precisely that concern underlies rapeshield statutes. See State v. Pulizzano, 155 Wis.2d 633, 456 N.W.2d 325, 330 (1990). Perhaps for that reason, the Supreme Court has never deemed a rape-shield statute unconstitutional. Hammer v. Karlen, 342 F.3d 807, 812 n. 6 (7th Cir.2003). And it would not be unreasonable for the Wisconsin court to conclude, after balancing the competing interests, that the evidence was inadmissible for any relevant purpose. See Dunlap v. Hepp, 436 F.3d 739, 745 (7th Cir.2006); Hammer, 342 F.3d at 812; Pack v. Page, 147 F.3d 586, 589 (7th Cir.1998). Similarly, it is hard to see how the Wisconsin courts would be unreasonable in concluding that Jardine had no constitutional right to impeach McKay rather than Grandhagen with evidence of prostitutionunless the Wisconsin courts were gravely mistaken in twice characterizing McKay's role in the trial as inconsequential.
At all events, portraying Grandhagen as promiscuous, or poking holes in her and McKay's testimony, would not solve Jardine's biggest problem: Grandhagen's vicious head wound, acquired on the evening he admittedly had sex with and shot her, and inflicted in a manner consistent with pistol-whipping with the butt of a gun like his.

III.
Despite the police misconduct that sparked Jardine's petition, the law requires that we AFFIRM the judgment of the district court.
NOTES
[1]  The record is thin because the district court granted a certificate of appealability after summarily dismissing the petition. Although district courts need not review state-court transcripts and pleadings in many § 2254 proceedings, including those involving Brady claims, see Simental v. Matrisciano, 363 F.3d 607, 612 (7th Cir.2004), and although summary dismissal without the warden's response has been commonplace for years, see, e.g., Small v. Endicott, 998 F.2d 411, 414 (7th Cir. 1993), common sense says that coupling summary dismissal with a certificate of appealability is poor practice. The conclusion that a constitutional claim is debatable among reasonable jurists, as required for a certificate of appealability under 28 U.S.C. § 2253(c), see Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000), sits in obvious tension with the conclusion that the claim "plainly appears" from the petition and attachments to be a loser, as required for summary dismissal under Rule 4 of the Rules Governing Section 2254 Cases in the United States District Courts. All the more so if, as here, the district court premises the certificate on reasonable debate about the import of suppressed evidence in light of all the other evidence.

Further, the district court's approach to this case spawned an appeal that was likely avoidable. If the state-court records turned out to give the warden a slam-dunk on the timeliness or fair-presentment issues, then no certificate of appealability should have issued, regardless of the merits. See Slack, 529 U.S. at 485, 120 S.Ct. 1595; Davis v. Borgen, 349 F.3d 1027, 1029 (7th Cir.2003); Anderson v. Litscher, 281 F.3d 672, 674 (7th Cir.2002). Moreover, a remand in these circumstances would still need to include time for the warden to develop the record and raise affirmative defenses. See Ray v. Boatwright, 592 F.3d 793, 798-99 (7th Cir.), cert. denied, ___ U.S. ___, 131 S.Ct. 595, 178 L.Ed.2d 434 (2010).
Because Jardine does not challenge the state court's characterization of his testimony, and because the state-court decisions and Jardine's petition give us enough for review on the merits, these considerations do not change the outcome today. Still, we respectfully advise district judges who plan on issuing a certificate of appealability to avoid Rule 4 and let the warden respond to the petition with exhibits.
[2]  Potentially, Jardine's claim about the gun could also be framed as one of ineffective assistance of counsel, as the district court suggested in its order granting a certificate of appealability. But Jardine's brief ignores that theory. At all events, declining to request DNA testing can be sound strategy when weaknesses in a defendant's story could lead reasonable lawyers to think the client guilty and any test results potentially damning. See Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 789-90, 178 L.Ed.2d 624 (2011).
