
586 F.3d 479 (2009)
Larry GEORGE, Petitioner-Appellant,
v.
Judy P. SMITH, Warden, Respondent-Appellee.
No. 07-3011.
United States Court of Appeals, Seventh Circuit.
Argued January 8, 2009.
Decided October 27, 2009.
*480 Christie O. Tate (argued), Skadden, Arps, Slate, Meagher & Flom, Chicago, IL, for Petitioner-Appellant.
Larry George, pro se.
William L. Gansner (argued), J.B. Van Hollen, Office of the Attorney General, Wisconsin Dept. of Justice, Madison, WI, for Respondent-Appellee.
*481 Before EASTERBROOK, Chief Judge, and EVANS and TINDER, Circuit Judges.
TINDER, Circuit Judge.
In 2001, Larry George was convicted in Wisconsin of two counts of second degree sexual assault by use of force, Wis. Stat. § 940.225(2)(a), and one count of false imprisonment, Wis. Stat. § 940.30. George wended his way through Wisconsin's appeal and postconviction procedures but was rebuffed at every point. After running out of options in Wisconsin, he filed a federal petition for habeas corpus in the Eastern District of Wisconsin. The district court denied the petition as well as George's request for a certificate of appealability.
On appeal, we granted George a certificate of appealability allowing him to present a Confrontation Clause challenge based on his counsel's inability to crossexamine the complaining witness who accused him of sexual assault. (The nature of the charges here causes us to refer to this man anonymously as the victim throughout the opinion). On appeal, George's counsel finds no merit in that claim and challenges instead the effectiveness of George's trial counsel.
George argues that his trial counsel failed to understand Wisconsin's rape shield law and therefore mistakenly did not object when the prosecutor improperly questioned the victim about the victim's sexual orientation. Furthermore, George argues, once the victim testified that he was heterosexual, George's trial counsel should have impeached the witness's claim with the testimony of another man who George claims had a homosexual encounter (or relationship) with the victim. George argues that his trial counsel's failure to pursue this line of inquiry was an error that rendered his trial counsel's assistance constitutionally deficient. We disagree.

I. Background
George's convictions arose from an incident on New Year's Eve in 1995. George and an accomplice abducted the victim (after a fight with the man and his friends) as he walked home from a bar in Appleton, Wisconsin. They took the man to the accomplice's house, had a few beers, and then George and the man took a cab to a motel in Green Bay and George checked in under an alias. At the motel, according to the jury's verdict, George assaulted the man twice, forcing him to perform oral sex both times. The next morning, George drove the man back to his job at a restaurant, where the man spoke to the police (who were alerted to the abduction by the man's friends). After initially denying that he was assaulted, the man eventually admitted to police, over a series of interviews, that George had assaulted him in the motel room.
Problems in the case against George are readily apparent after a glance at that sequence of events. For instance, why did the evening begin with a fight and end with the two combatants checking into a motel together? Why did the victim ride back to work with George the morning after being assaulted? Why did the victim's story change? At George's trial, defense counsel attacked these areas of inconsistency, focusing on the number of differing stories the victim told the police and noting, for the jury, the multiple chances the victim had to escape George's clutches. Notably, however, George's defense was not based on consent; instead, George's counsel argued that even though George and the victim had stayed in the hotel together (a fact that was impossible to dispute), no sexual assault occurred and the victim had made the entire story up to *482 avoid paying a $900 debt. It was this debt, incidentally, that initially led George and his accomplice to track the victim down.
For his part, the prosecutor offered an explanation for the victim's continued travels with George over the course of the evening by pointing out that the two had an incentive to collaborate to some extent after the fight because they both had outstanding warrants and therefore sought to avoid the police, who had been alerted by the victim's roommates. The prosecutor then attempted to rehabilitate the victim's credibility, which had been damaged by his shifting versions of events that night, by asking the victim whether he was heterosexual. The victim said he was and that he was embarrassed about reporting a homosexual assault, which accounted for his initial less-than-forthcoming interviews with the police and the resulting inconsistencies in his account of what happened that evening. The prosecutor emphasized this rationale during his closing argument.
George was convicted. He unsuccessfully sought postconviction review in the Wisconsin trial court, arguing, among other things, that his trial counsel was ineffective. On appeal from the denial of his postconviction motion and his conviction, he maintained his ineffectiveness claims and asserted that the prosecutor violated Wisconsin's rape shield statute when he elicited testimony from the victim about his sexual orientation. The Wisconsin appeals court rejected the rape shield claim holding that "[s]exual orientation is not conduct or reputation" as defined in the rape shield statute, Wis. Stat. § 972.11(2)(b). State v. George, No. 03-0299-CR, 2004 WL 1276965, at *2 (Wis.Ct. App.2004). His other claim, that the failure to cross-examine the victim rendered his counsel ineffective, was not so neatly addressed. The Wisconsin Court of Appeals threw out a number of his ineffectiveness claims as abandoned or waived, but did not specify which claims fell into this category. The court rejected several others because George did not call appropriate witnesses at the postconviction hearing. (As we will discuss, we believe that this group of claims includes the failure to cross-examine issue George raises before us). The court rejected another set of ineffectiveness claims because George could not establish prejudice resulting from his counsel's decisions. The Wisconsin Supreme Court denied George's petition for review.
George then sought review in the Eastern District of Wisconsin. There, he raised a number of issues, including the two before us, but in a different form. He argued that he was entitled to a writ because the state violated its own rape shield law in prosecuting him. He also argued that his inability to cross-examine the victim about his sexual orientation violated the Confrontation Clause. The district court rejected the rape shield claim, noted that the Confrontation Clause argument did not make sense because George had an opportunity to fully cross-examine the victim, and then construed the cross-examination issue as an ineffectiveness issue, which the district court also rejected. The court denied the writ and refused to issue a certificate of appealability.
On appeal, we issued a certificate of appealability, finding that "George has made a substantial showing of the denial of a constitutional right as to whether the state trial court violated his rights under the confrontation clause when it did not permit him to cross-examine the victim about a prior homosexual relationship."

II. Analysis

A. Amendment of Certificate of Appealability
As a threshold matter, we grant George's request to amend the certificate *483 of appealability so that he may address the Sixth Amendment issues he raises in his briefs. As we have noted in the past, amendment of the certificate is appropriate even if the petitioner makes the request in his brief on appeal in the "rare instances where the importance of an issue does not become clear until later in an appellate proceeding." Ouska v. Cahill-Masching, 246 F.3d 1036, 1046 (7th Cir. 2001). George was not represented by counsel in the district court, cf. id. at 1046 n. 8, but he did raise the issues before us here: the rape shield and failure to cross-examine claims. Both issues, as his counsel notes, are more properly framed as a challenge to his counsel's effectiveness (rather than as Confrontation Clause issues), and we thus are inclined to amend the certificate of appealability to squarely address the issues that George's counsel seeks to raise.
Wisconsin argues that George has not made "a substantial showing of the denial of a constitutional right as to a different issue," justifying the amendment of the certificate. See id. at 1045. The question is whether George has demonstrated "that reasonable jurists could debate whether this challenge in [his] habeas petition could have been resolved in a different manner or that the issue presented was adequate to deserve encouragement to proceed further." Id. at 1046. Given that we have already granted a certificate of appealability wherein we asked George to address any Confrontation Clause issues stemming from his inability to cross-examine the victim about a prior homosexual relationship, we believe the consequence of the issue justifies consideration. The constitutional import of the issue survives when we examine the issue through the prism of an ineffective assistance claim because the credibility of the victim was the key issue in the case; failings in this area could have affected the trial's outcome. Therefore, we believe that George has made a sufficient showing to allow expansion of the certificate of appealability, and proceed to an analysis of the case.

B. Constitutional Effectiveness of George's Trial Counsel
George asks for a writ of habeas corpus under 28 U.S.C. § 2254 on the grounds that he was convicted without the effective assistance of counsel in violation of the Sixth Amendment. "The benchmark for judging any claim of ineffectiveness must be whether counsel's conduct so undermined the proper functioning of the adversarial process that the trial cannot be relied on as having produced a just result." Strickland v. Washington, 466 U.S. 668, 686, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). To establish that his counsel's performance was constitutionally ineffective, George must show that his counsel's performance was below an objective standard of reasonableness and that the deficient performance actually prejudiced him. Id. at 687, 104 S.Ct. 2052.

1. Rape Shield Claim
We can quickly dispense with George's claim that his lawyer should have objected when the prosecutor elicited testimony from the victim about his sexual orientation. George raised this claim below (and in Wisconsin) on the grounds that his conviction was secured through a violation of state law. This, of course, does not make out a claim for habeas relief under 28 U.S.C. § 2254, which covers only prisoners in custody "in violation of the Constitution or laws or treaties of the United States." 28 U.S.C. § 2254(a); see Lambert v. Davis, 449 F.3d 774, 778-79 (7th Cir.2006) (citing Estelle v. McGuire, 502 U.S. 62, 68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991)). Converting the claim to an ineffective *484 assistance claim would not get him anywhere either. The Wisconsin Court of Appeals agreed with his lawyer's interpretation of the statute and found that the evidence was properly admitted. We are obviously not going to displace Wisconsin's interpretation of its own law with our own, much less find George's counsel ineffective for adopting a view of Wisconsin law that has been ratified by the state's appeals court. See Mullaney v. Wilbur, 421 U.S. 684, 691, 95 S.Ct. 1881, 44 L.Ed.2d 508 (1975) ("[S]tate courts are the ultimate expositors of state law and ... we are bound by their constructions except in extreme circumstances not present here." (citation omitted)). This claim must therefore fail.

2. Failure to Cross-Examine Claim
The parties dispute whether George's failure to cross-examine claim was reached on the merits in Wisconsin court, although the state does not dispute that the issue has been properly preserved. Whether the state courts reached the issue matters only for the purpose of the standard of review we should apply.
George raised this ineffectiveness issue in an identical form in the Wisconsin courts in his postconviction motion for a new trial, his brief on his direct appeal to the Wisconsin court of appeals, his reply brief on direct appeal, and his petition to the Wisconsin Supreme Court. If any of the Wisconsin courts ruled on the merits of the issue, our review is constrained by the Anti-Terrorism and Effective Death Penalty Act (AEDPA), 28 U.S.C. § 2254(d)(1). See Canaan v. McBride, 395 F.3d 376, 382 (7th Cir.2005) ("[The AEDPA] standard only applies ... to a claim that was adjudicated on the merits in State court proceedings." (quotation omitted)). If AEDPA does not apply, we review the state court decisions "as law and justice require," a more generous standard. Id. at 383 (quoting 28 U.S.C. § 2243).
The district court found that the ineffectiveness issues had been ruled on by the Wisconsin Court of Appeals and that the court held that the decision not to impeach the complaining witness was one of strategy. Such an application of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the district court found, was not unreasonable or contrary to Supreme Court precedent. We are not sure that the state court was so clear about this issue. The Wisconsin court divided George's claims into five classes, ranging from general claims of ineffectiveness to more specific allegations of failure. It appears that the specific claim before usthe failure to cross-examine claim was treated in the former class of general claims of ineffectiveness. The court wrote:
Several of George's claims of ineffective assistance failed because he did not call appropriate witnesses at the postconviction hearing. The only witnesses called at the postconviction hearing were George, his trial attorney and an Appleton police officer who investigated the [George's] uncharged earlier incidents of sexual assault and intimidation by weapons. None of these witnesses' testimony established trial counsel's deficient performance or prejudice. George alleges ineffective assistance because his counsel failed to investigate some defenses, did not call witnesses to support those defenses and did not effectively cross-examine [the victim] about drinking and drug use. He faults his counsel for not producing jail inmates to impeach [the victim's] testimony and for not locating other motel guests to learn whether they heard anything during the assaults. To prevail on these issues, George was required to call these witnesses at the Machner hearing to establish that they were willing to testify and that they *485 would have provided exculpatory information. Without the testimony from these witnesses, it would be pure speculation to conclude that his defense was prejudiced by his counsel's failure to present their testimony.
George, 2004 WL 1276965, at *2, ¶ 10 (footnote omitted).
There's a lot therebut notably missing is an analysis of the specific claim we are considering here. We could infer, as the district court did, that the Wisconsin court found that the absence of witnesses doomed the claim, but we hesitate to apply a stricter standard of review without a clearer indication that Wisconsin fully considered George's claim on the merits. See Canaan, 395 F.3d at 382 ("As a practical matter, a federal court cannot apply the deferential standard provided by § 2254(d) in the absence of any state court decision on the issue."); see also Wiggins v. Smith, 539 U.S. 510, 534, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) ("In this case, our review is not circumscribed by a state court conclusion with respect to prejudice, as neither of the state courts below reached this prong of the Strickland analysis.").
Unfortunately for George, our standard of review matters little because even under the more generous standard, the claim must fail. At the outset, we note that we can conceive of a case in which a failure to impeach a testifying victim who lied about his sexual orientation would satisfy the Strickland test for deficient performance causing prejudice to the defendant. The problem for the defendant here is that he has given us no reason to think that this is that case.
From the petitioner's brief, here is the entire factual basis of George's ineffectiveness claim:
During the postconviction hearing, Mr. George testified that he told counsel, prior to trial, that [the victim] had had a homosexual relationship with someone at the restaurant where he worked:
Question: Did you tell [trial counsel] that [the victim] had had a homosexual relationship with someone at Apollon Restaurant?
Mr. George: Yes, I did.
Pet'r Br. 31.
This is not enough. "To be entitled to federal habeas relief from a state court judgment, a petitioner must show that he is being held in violation of the Constitution or laws of the United States." Gross v. Knight, 560 F.3d 668, 671 (7th Cir.2009) (emphasis added). To prevail on an ineffective assistance of counsel claim, George "must show that (1) his counsel's performance was deficient; and (2) this deficient performance prejudiced him." Id. (emphasis added). The responsibility is on the petitioner to "overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy." Strickland, 466 U.S. at 689, 104 S.Ct. 2052 (quotation omitted). It is incumbent on the petitioner to "identify the acts or omissions of counsel that are alleged not to have been the result of reasonable professional judgment." Id. at 690, 104 S.Ct. 2052. Similarly, the petitioner must "affirmatively prove" the prejudice prong of his Strickland claim and "show that [the errors] actually had an adverse effect on the defense." Id. at 693, 104 S.Ct. 2052 (emphasis added). "To demonstrate prejudice from counsel's deficient performance, `a defendant must show that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different.'" Pole v. Randolph, 570 F.3d 922, 934 (7th Cir.2009) (quoting Strickland, 466 U.S. at 694, 104 S.Ct. 2052) (emphasis added). "If a defendant is unable to make a sufficient showing on either component *486 of the Strickland standard, we need not consider the other component." Id. (emphasis added).
In other words, in Strickland, the Supreme Court made clear that a habeas petitioner has an obligation to show us why his counsel was ineffective. George just hasn't done so. Keep in mind that we are the fifth court to consider this claim. Petitioner has to give us some specific reason to believe that the other four courts got it wrong and that he is being detained in violation of the Constitution. Speculation based on hindsight is insufficient to make this showing. See Strickland, 466 U.S. at 689, 104 S.Ct. 2052. Here, in order for us to grant the writ George seeks, he needs to offer some basis for us to believe that a witness was available to testify to the victim's sexual orientation and that there was a reasonable probability that this witness's testimony would have made a difference in the outcome of the trial. We have no idea who would testify about the victim's sexual orientation, the nature of the witness's relationship with the victim, or any hint as to the credibility of the testimony.[1] All of these factors would be important to both prongs of the Strickland analysis.
Perhaps George would argue that the problem is not his counsel's failure to interrogate a particular witness but rather that his counsel should have pursued the leads that George offered him. For such a claim, he would need to prove that there was a witness who could have testified credibly about the victim's sexuality, that his counsel knew or should have known about the witness, and that there was a reasonable probability that such a witness's testimony would have made a difference in the outcome of his case. See id. at 690-91, 104 S.Ct. 2052. Once again, George's hint that there was a coworker of the victim who had a homosexual encounter or relationship with the victim is not enough.
Faced with this need to affirmatively prove the ineffectiveness of his counsel, George has only offered us a reed that is far too thin to support his "failure to investigate" claim. See id. at 691, 104 S.Ct. 2052 ("[A] particular decision not to investigate must be directly assessed for reasonableness in all the circumstances, applying a heavy measure of deference to counsel's judgments."). Given the sparsity of details, we are unprepared to make a blanket assumption that a victim of a homosexual assault would necessarily be effectively impeached by revelations of a prior homosexual relationship. The relevance of the prior sexual relationship to the homosexual assault and the shame associated *487 in reporting it is not obvious and should have been developed by the petitioner. It seems to us that, for instance, a homosexual man may be just as embarrassed about reporting sexual assault as a heterosexual man who suffered the same assault. As such, without more facts, George cannot show that counsel's failure to impeach the victim's testimony regarding his sexual orientation was unreasonable or prejudicial.
Finally, we should mention that George's case did not turn in any sense on the sexual orientation of the victim. The defense George offered was not a consent defense. He denied that the assault ever happened and that the victim made it up to avoid paying a debt of $900 (the debt led to the initial confrontation on the streets of Appleton). But, George could not overcome the undisputed evidence at trial that showed that he was involved in an altercation at the victim's house, that the victim's abduction was serious enough for his friends to call the police, and that George took the victim to a hotel room in Green Bay. A consent defense may have made sense in clearing up the details within the evening's undisputed time frame (for example, it could have been argued that the evidence tended to show that the evening turned from a hostile one to a more companionable one). But the trial strategy was instead a direct attack on the victim's entire story. The choice to pursue this defense is not challenged and such a decision falls squarely within the realm of trial strategy and is thus subject to a strong presumption that the decision constituted effective advocacy. See id. at 689, 104 S.Ct. 2052; Smith v. Gaetz, 565 F.3d 346, 354 (7th Cir.2009) ("It is not this court's role to play Monday-morning quarterback concerning which was the better of two viable trial strategies."). At no point, not even in this court, does George assert that he had a consensual sexual encounter with the victim; perhaps because that is not true or perhaps because he would find such an assertion embarrassing or compromising of some other relationship. But there is no point in speculating about a defense that was not pursued. In the context of the defense George did present, the complaining witness's sexual orientation was at best a side issue. Failure to pursue this line of inquiry was not unreasonable and George's conviction was therefore not a result of a breakdown in the adversary process. Id. at 687, 104 S.Ct. 2052.

III. Conclusion
Accordingly, the district court's denial of George's petition is AFFIRMED.
NOTES
[1]  Perhaps sensing the fundamental problem with his claim, George sought to supplement the record on appeal (ostensibly (continued...) to correct his counsel's statements at oral argument) by introducing affidavits from witnesses who swore that they would testify to the victim's homosexuality. But George originally produced the affidavits in connection with a state court motion for a new trial that was filed after the district court had already denied his petition for the writ. They were not presented to us until after argument. We have allowed a habeas petitioner to supplement the record on rare occasions, but only when the information included was important to an understanding of the prior proceedings in a plaintiff's case. See, e.g., Crockett v. Hulick, 542 F.3d 1183, 1188 n. 3 (7th Cir.2008); Ruvalcaba v. Chandler, 416 F.3d 555, 562 n. 2 (7th Cir.2005). Here, the evidence George seeks to admit is essentially brand new; it was only offered to the Wisconsin trial court after the beginning of George's federal habeas proceeding. Accordingly, it is not evidence "omitted from or misstated in the record by error or accident", Fed. R.App. P. 10(e)(2), and we denied the motion to supplement the record on appeal. Our decision, of course, does not preclude George from continuing to seek a new trial based on procedures, if any, provided to him by Wisconsin.
