In December 2010 a Wisconsin jury found Muhammad Sarfraz guilty of sexually assaulting I.N., a Pakistani immigrant who, along with her father, briefly lived with Sarfraz after arriving in this country in late 2009. 1 At trial I.N. described a violent assault in which Sarfraz forced his way into her apartment, strangled her, threatened her with a knife, and raped her. Abundant physical evidence corroborated her account. Sarfraz claimed that I.N. consented to the sexual intercourse.

To support this defense, Sarfraz sought to introduce evidence that he and I.N. had previously engaged in consensual sexual contact while she and her father were living with him. The trial judge excluded this evidence under Wisconsin's rape-shield law. On appeal Sarfraz argued that the trial judge misapplied the rape-shield law and deprived him of his right to confront the witnesses against him and his right to present a defense. The state court of appeals reversed the conviction, State v. Sarfraz (" Sarfraz I "), 348 Wis.2d 57 , 832 N.W.2d 346 , 347 (App. 2013), but the Wisconsin Supreme Court reinstated it, reasoning that the State's interest in excluding the evidence outweighed Sarfraz's interest in admitting it, State v. Sarfraz (" Sarfraz II "), 356 Wis.2d 460 , 851 N.W.2d 235 , 247-48 (2014).

*1032 Sarfraz sought federal review under 28 U.S.C. § 2254 , again claiming that the judge's rape-shield ruling deprived him of his confrontation right and his right to present a defense. A magistrate judge denied relief but certified the issue for appeal.

We affirm. The state supreme court specifically noted but did not separately analyze Sarfraz's federal constitutional claims. That brings into play the Richter presumption, which requires us to treat the decision as an adjudication on the merits and review it deferentially under § 2254(d). Harrington v. Richter , 562 U.S. 86 , 99, 131 S.Ct. 770 , 178 L.Ed.2d 624 (2011). Applying that standard, we agree with the magistrate judge that habeas relief is unwarranted. The state court's decision did not involve an unreasonable application of federal law.

I. Background

I.N. and her father moved from Pakistan to Milwaukee in December 2009. A family member arranged for them to live temporarily with Sarfraz, another Pakistani immigrant who worked as a taxi driver. I.N. and her father stayed at the apartment that Sarfraz shared with his wife and children for about two and a half months before moving to their own apartment.

On May 15, 2010, Sarfraz unexpectedly showed up at I.N.'s new apartment. At trial they gave dramatically different accounts of what happened that day. I.N. testified that she heard a knock on the door that morning. She asked who it was, and the person outside the door answered "Jim," which was her landlord's name. She opened the door and saw a masked man standing in the hallway. He forced his way into the apartment, pushed her into the bathroom, and began choking her, saying, "I'll kill you." He then pulled a knife from his pocket and held it to her neck. I.N. managed to pull the mask from the man's face and recognized Sarfraz. At some point during the struggle in the bathroom, Sarfraz set the knife on the floor. I.N. grabbed it, cutting her finger in the process, and slashed him on the cheek. Blood covered the bathroom floor.

Sarfraz took the knife from I.N. and began to choke her again. As she continued to struggle, Sarfraz tried to hit her, pulled at her breasts, and eventually tied a handkerchief around her mouth in an effort to quiet her. He tried to take her into the bedroom, but she resisted and the two ended up in the living room. There Sarfraz produced a pornographic DVD he brought with him and tried to make her watch it. He then shoved her onto the floor, removed her pants, began to fondle her genitals, and eventually had forcible vaginal intercourse with her, all while she continued to resist. At some point during this ordeal, I.N. scrawled the first few letters of Sarfraz's last name in blood on a newspaper because she feared that she would not survive. Immediately after Sarfraz left, I.N. ran into the hallway and screamed for help.

A neighbor testified that his wife heard a commotion in I.N.'s apartment, and when he went to investigate, he saw I.N. standing in the hallway bloodied and naked from the waist down, screaming that she had been raped. He called 911.

The physical evidence introduced at trial supported I.N.'s account. In a search of her apartment, the police found a newspaper-and also a file cabinet-bearing the letters "S-A-R" written in blood, as well as a pornographic DVD. Officers recovered a bloody knife from Sarfraz's taxicab; forensic testing revealed the presence of DNA matching both I.N. and Sarfraz. Immediately after the attack, I.N. was examined by a sexual-assault nurse. The nurse noted that she had cuts on her finger and ankle, injuries to her vaginal area consistent with *1033 trauma, and tenderness at the front of her throat consistent with strangulation. The nurse also performed a vaginal swab, and forensic testing revealed the presence of Sarfraz's semen.

Sarfraz was arrested and charged with second-degree sexual assault by use of a dangerous weapon. See WIS. STAT. §§ 940.225(2)(a), 939.63(1)(b). He claimed that I.N. consented to the sexual intercourse. Before trial he moved to admit evidence of a prior intimate relationship with I.N. The State opposed the motion based on Wisconsin's rape-shield statute. After an evidentiary hearing, the trial judge concluded that the rape-shield law barred evidence of prior sexual contact between Sarfraz and I.N. But the judge gave Sarfraz substantial latitude to present evidence of a prior romantic relationship with I.N.

More specifically, the judge permitted Sarfraz to testify that when I.N. and her father lived with his family, he and I.N. hugged and kissed each other when his wife was not home, and also had watched pornographic videos together a few times. Sarfraz was allowed to testify that he and I.N. had planned to marry and that he did not need to divorce his wife to marry her because in his culture he could have multiple wives. He told the jury that I.N. and her father moved out when they did only because Sarfraz's wife caught him in bed with I.N. and became angry. Lastly, Sarfraz was permitted to testify that he gave I.N. money, helped her find a new apartment, and visited her regularly once she moved.

In short, the judge excluded only the most graphic sexual details of Sarfraz's testimony about their prior relationship. In particular, the judge precluded Sarfraz from testifying that he and I.N. had engaged in fondling and mutual masturbation but had agreed not to escalate to intercourse because it was against their cultural norms to do so outside of marriage.

The judge also allowed Sarfraz to call other witnesses to support his consent defense. To that end, he presented testimony from his wife, Riffat Sarfraz, who told the jury that she twice came home early and discovered Sarfraz and I.N. in compromising situations. The first time she found Sarfraz and I.N. "lovingly" feeding each other. The second time she discovered I.N. and Sarfraz in bed together. The judge precluded her from testifying that neither was wearing pants. The judge did, however, allow her to testify that what she saw made her so emotional that she started throwing I.N.'s belongings out of the apartment and told her husband that I.N. had to move out. Indeed, I.N. and her father moved out a few days later.

Sarfraz also presented testimony from Azmath Uddin, a friend and fellow cab driver who told the jury that on two occasions he caught Sarfraz and I.N. together when he dropped by the apartment unannounced. On the first occasion, he saw I.N. sitting on Sarfraz's lap with her legs on either side of him and Sarfraz had his hands around her waist. On the second occasion, Uddin saw I.N. hugging Sarfraz from behind.

The judge also permitted Sarfraz's attorney to cross-examine I.N. about a romantic relationship between them. She denied it. The judge allowed limited follow-up cross-examination on this subject-for example, defense counsel was permitted to ask if she and Sarfraz had ever hugged or kissed. She denied this too.

Sarfraz's version of the events of May 15 was starkly different from I.N.'s testimony. He testified that I.N. was the initial aggressor and also initiated the sex. He told the jury that he went over to I.N.'s apartment without a mask, knife, or pornographic DVD. They visited inside the *1034 apartment, and the conversation turned to marriage. I.N. told Sarfraz that she did not want to marry him unless he left his wife and children. When he told her that was impossible, she became "furiously mad." She began crying and yelling, grabbed Sarfraz's collar, and started hitting him with her fists. Sarfraz had a sudden urge to urinate (owing to a health condition), and he hurriedly pushed I.N. out of the way to get to the bathroom. She then barged into the bathroom wielding a knife and slashed him on the face while he was sitting on the toilet. A struggle ensued. Sarfraz tried to get the knife away from her, and she cut her finger as they tussled over it. Sarfraz pushed her out of the bathroom with his hands on her throat. At some point he succeeded in taking the knife away from I.N. and put it in his pocket.

Sarfraz testified that he then returned to the living room and collapsed on the floor, exhausted and in pain. He told I.N. that if he called the police on her, she could face immigration problems, and she started crying and apologizing. Sarfraz's pants were still down from using the toilet, and I.N. sat on top of him and started "love talk." She told him that she wanted to have sex. Initially he resisted, but she put on a pornographic video, took off her shirt and pants, and started groping him. He said he was "not sure" if his penis ever entered her vagina, but he did ejaculate "close to her vagina." After he ejaculated, he wiped up the blood on the floor with a cloth, and I.N. got dressed. He then hugged her and left the apartment. To explain his injuries to his wife, his friend Uddin, and later a detective, he made up a story that he had been robbed.

The jury found Sarfraz guilty. A divided state appellate court reversed, holding that Wisconsin's rape-shield statute did not bar the evidence of prior sexual contact between Sarfraz and I.N. Sarfraz I , 832 N.W.2d at 347 . The Wisconsin Supreme Court granted review and reversed the appellate court. Sarfraz II , 851 N.W.2d at 238 .

The state high court began its analysis by explaining that Sarfraz's appeal presented two interrelated questions: (1) whether the trial court erred in excluding the proffered evidence under the Wisconsin rape-shield law; and (2) whether the exclusion of this evidence violated Sarfraz's right to present a defense or his right to confront adverse witnesses, both of which are guaranteed to him under the U.S. and Wisconsin Constitutions. Id. at 242-43 (citing the Sixth Amendment and Article I, Section 7 of the Wisconsin Constitution ). The court then turned its attention to the terms of the rape-shield statute and the court's precedents applying it.

The rape-shield law applies in specified sex-crime prosecutions and generally bars evidence about the complaining witness's prior sexual history, subject to certain exceptions. WIS. STAT. § 972.11(2)(b). One exception permits evidence of a complainant's past sexual conduct with the defendant. Id. § 972.11(2)(b)1. The court explained that to introduce evidence under this exception, the defendant must show that: "(i) the proffered evidence relates to sexual activities between the complainant and the defendant; (ii) the evidence is material to a fact at issue; and (iii) the evidence of sexual contact with the complainant is of 'sufficient probative value to outweigh its inflammatory and prejudicial nature.' " Sarfraz II , 851 N.W.2d at 244 (quoting State v. Jackson , 216 Wis.2d 646 , 575 N.W.2d 475 , 481 (1998) ).

The court concluded that Sarfraz had carried his burden under the first part of the test because a reasonable person could find that it was more likely than not that a sexual relationship existed between I.N. and Sarfraz. Id. He also satisfied the second *1035 part of the test because his evidence of prior sexual contact with I.N. had some probative value on the issue of I.N.'s credibility and Sarfraz's consent defense. Id. at 244-47. But Sarfraz did not carry his burden at the third step in the analysis.

The court explained that the final step in the tripartite framework asks whether the evidence of prior sexual contact between the complainant and the defendant "has sufficient probative value to outweigh its inflammatory and prejudicial nature." Id. at 247. The court described this inquiry as an "inverted balancing test" that assumes, "absent an evidentiary showing to the contrary, [that] the proffered evidence is more prejudicial than probative." Id. at 247-48 (quoting Jackson , 575 N.W.2d at 481 ) (alteration in original). The inverted balancing test, the court said, serves the statute's purpose by "protect[ing] complainants from the embarrassment and humiliation that discourage[ ] victims from reporting crimes of sexual assault." Id.

Applying the inverted balancing test, the court reasoned that the proffered evidence of prior sexual contact between Sarfraz and I.N. had very little probative value on the issues of I.N.'s credibility in general and the consent defense in particular. The prior conduct (assuming it occurred) consisted only of fondling and mutual masturbation, which was vastly different from vaginal intercourse after a knife fight. Id. at 247. In the court's view, Sarfraz's evidence of a prior relationship limited to sexual contact short of intercourse might even have a tendency to undermine his argument that I.N. consented to have intercourse on the date in question. Id. at 248. The court concluded that the minimal probative value of the proffered evidence was not enough to overcome the strong starting presumption that the evidence was more prejudicial than probative. After holding that the evidence was properly excluded, the court reversed and remanded for consideration of Sarfraz's previously unaddressed claims of sentencing error and ineffective assistance of counsel. Id. at 248. The court did not separately analyze the constitutional claims.

Sarfraz then moved his case to federal court on a § 2254 petition for habeas corpus. He again asserted that the trial judge's rape-shield ruling deprived him of his right to confront witnesses and his right to present a defense. A magistrate judge, presiding by consent, denied relief but issued a certificate of appealability authorizing this appeal.

II. Discussion

We review the magistrate judge's denial of § 2254 relief de novo. Peterson v. Douma , 751 F.3d 524 , 529 (7th Cir. 2014). On habeas review of a state-court judgment, a federal court may not grant relief unless the state court's decision was "contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," or was "based on an unreasonable determination of the facts in light of the evidence presented in the [s]tate court proceeding." 28 U.S.C. § 2254 (d)(1), (2). To prevail under this standard, "a state prisoner must show that the state court's ruling on the claim being presented in federal court was so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement." Ward v. Neal , 835 F.3d 698 , 703 (7th Cir. 2016) (quoting Richter , 562 U.S. at 103 , 131 S.Ct. 770 ).

Sarfraz argues that § 2254(d) 's deferential standard does not apply because the state supreme court's decision addressed Wisconsin's rape-shield law but never expressly circled back to consider his constitutional claims. That argument is foreclosed by the Supreme Court's decisions *1036 in Richter and Johnson v. Williams , 568 U.S. 289 , 133 S.Ct. 1088 , 185 L.Ed.2d 105 (2013).

To begin, § 2254(d) 's deferential standard of review applies only to claims that a state court has "adjudicated on the merits." In Richter the Court considered whether § 2254(d) applies when a state court denies relief in a one-sentence summary order without any explanation. 562 U.S. at 98 , 131 S.Ct. 770 . The Court held that when a defendant presents a federal claim to a state court and the state court denies relief, the federal habeas court should presume that the state court adjudicated the claim on the merits. Id. at 99 , 131 S.Ct. 770 . The presumption can be overcome, but only "when there is reason to think some other explanation for the state court's decision is more likely." Id. at 99-100 , 131 S.Ct. 770 . The state prisoner has the burden to rebut the presumption, and because he could not make the required showing, the Court applied § 2254(d) 's deferential standard. Id. at 100 , 131 S.Ct. 770 .

In Williams the Court applied the Richter presumption in a situation closely analogous to Sarfraz's. 568 U.S. at 295-96 , 133 S.Ct. 1088 . There, as here, the habeas petitioner had presented a federal claim in her state-court appeal. Id. at 295 , 133 S.Ct. 1088 . The state court denied relief in an opinion addressing some of her claims but without expressly analyzing the federal claim that she later raised in her § 2254 petition. Id. at 295-96 , 133 S.Ct. 1088 . The Court invoked the Richter presumption but explained that it can be overcome "[w]hen the evidence leads very clearly to the conclusion that a federal claim was inadvertently overlooked in state court." Id. at 303 , 133 S.Ct. 1088 . In the case before the Court, the state appellate court had expressly relied on a decision of the state supreme court, which in turn had relied on three federal cases. Id. at 304 , 133 S.Ct. 1088 . In addition, the state-law claim that the state court did address was quite similar to the federal claim that went unmentioned; the overlap was so significant that it was "difficult to imagine any panel of appellate judges" failing to recognize the federal dimension of the issue. Id. at 305-06 , 133 S.Ct. 1088 . Under these circumstances, the Court found it "exceedingly unlikely" that the state appellate court had inadvertently overlooked the federal claim. Id. at 306 , 133 S.Ct. 1088 .

It follows from Richter and Williams that we should treat the Wisconsin Supreme Court's decision as a merits adjudication of Sarfraz's federal claims. Indeed, the state supreme court specifically described the federal claims, explicitly recognizing that Sarfraz's evidentiary argument had federal constitutional dimensions. 851 N.W.2d at 242-43 . The court went on to explain that in certain circumstances, the Sixth Amendment requires the admission of evidence that would otherwise be excluded under the rape-shield law. To support this proposition, the court invoked State v. Pulizzano , 155 Wis.2d 633 , 456 N.W.2d 325 , 330-31 (1990), which in turn relied on Chambers v. Mississippi , 410 U.S. 284 , 294-95, 302, 93 S.Ct. 1038 , 35 L.Ed.2d 297 (1973), and Davis v. Alaska , 415 U.S. 308 , 318, 94 S.Ct. 1105 , 39 L.Ed.2d 347 (1974). So here, as in Williams , the evidence does not "very clearly" show that the Wisconsin Supreme Court inadvertently overlooked Sarfraz's federal claims. To the contrary, the evidence points in the opposite direction: the court was plainly aware of the significant overlap between the statutory and constitutional claims. The Richter presumption applies, and our review is governed by § 2254(d) 's deferential standard.

Applying Richter requires us to "give the state-court judgment the benefit of any arguments or theories that could *1037 have supported the state court's judgment." Adorno v. Melvin , 876 F.3d 917 , 919 (7th Cir. 2017) (citing Richter , 562 U.S. at 102 , 131 S.Ct. 770 ). Sarfraz argues that the excluded evidence was so crucial to his defense that the state court's ruling was an unreasonable application of Supreme Court precedent on the confrontation right and the right to present a defense. We are not persuaded.

The Sixth Amendment guarantees the right of an accused to be confronted with the witnesses against him; this includes the right to cross-examine adverse witnesses. Davis , 415 U.S. at 315 , 94 S.Ct. 1105 . The Fourteenth Amendment's Due Process Clause and the Compulsory Process Clause of the Sixth Amendment protect a defendant's right to testify in his defense. Rock v. Arkansas , 483 U.S. 44 , 51-52, 107 S.Ct. 2704 , 97 L.Ed.2d 37 (1987). "Whether rooted directly in the Due Process Clause of the Fourteenth Amendment or in the Compulsory Process or Confrontation Clauses of the Sixth Amendment, the Constitution guarantees criminal defendants 'a meaningful opportunity to present a complete defense.' " Holmes v. South Carolina , 547 U.S. 319 , 319, 126 S.Ct. 1727 , 164 L.Ed.2d 503 (2006) (quoting Crane v. Kentucky, 476 U.S. 683 , 690, 106 S.Ct. 2142 , 90 L.Ed.2d 636 (1986) ).

It's well established, however, that the constitutional rights to cross-examine witnesses and present relevant testimony are not absolute; these rights "may, in appropriate cases, bow to accommodate other legitimate interests in the criminal trial process." Rock , 483 U.S. at 56 , 107 S.Ct. 2704 (quoting Chambers , 410 U.S. at 295 , 93 S.Ct. 1038 ). But restrictions on a criminal defendant's right to cross-examine adverse witnesses and present evidence in his own defense "may not be arbitrary or disproportionate to the purposes they are designed to serve." Michigan v. Lucas , 500 U.S. 145 , 151, 111 S.Ct. 1743 , 114 L.Ed.2d 205 (1991) (quoting Rock , 483 U.S. at 56 , 107 S.Ct. 2704 ). These principles do not call into question the constitutionality of "well-established rules of evidence [that] permit trial judges to exclude evidence if its probative value is outweighed by certain other factors such as unfair prejudice, confusion of the issues, or potential to mislead the jury." Holmes , 547 U.S. at 326 , 126 S.Ct. 1727 ; see also Montana v. Egelhoff , 518 U.S. 37 , 42, 116 S.Ct. 2013 , 135 L.Ed.2d 361 (1996).

These are generally applicable constitutional principles. More directly on point here, we have twice upheld state-court rulings rejecting similar constitutional claims based on the exclusion of evidence under rape-shield laws. See Dunlap v. Hepp , 436 F.3d 739 (7th Cir. 2006) ; Hammer v. Karlen , 342 F.3d 807 (7th Cir. 2003). In each case the state court's decision gave substantial weight to the public interest in protecting sexual-assault complainants when weighing whether the exclusion of otherwise relevant evidence violated a defendant's rights under the Sixth Amendment. Dunlap , 436 F.3d at 745 ; Hammer , 342 F.3d at 812 .

So too here. The Wisconsin Supreme Court applied its "inverted balancing test" to determine whether Sarfraz's proffered evidence fell within an exception to the rape-shield law. As we've explained, the test starts from a strong presumption that evidence of a complainant's sexual history is more prejudicial than probative, giving significant weight to the public interest underlying any rape-shield law: "to protect complainants from the embarrassment and humiliation that discourage[ ] victims from reporting crimes of sexual assault." Sarfraz II , 851 N.W.2d at 248 . The court then evaluated the strength of Sarfraz's interest in presenting the proffered evidence, ultimately concluding that it was quite low. The excluded evidence, the court said, had *1038 only marginal probative value because it was so strikingly dissimilar from the charged crime. Id. at 247. Even assuming that Sarfraz's claims about fondling and mutual masturbation were true, it would not be appreciably more plausible that I.N. consented to vaginal intercourse on the living-room floor after a violent struggle and a bloody knife fight. Id.

In sum, the court concluded that the State's interest in excluding the evidence outweighed Sarfraz's interest in admitting it. As we've explained, the Supreme Court has held that the application of evidentiary rules limiting a defendant's right to cross-examine witnesses and present evidence may not be disproportionate to the purposes they are designed to serve. The Wisconsin Supreme Court's balancing of interests was not an unreasonable application of that standard.

This conclusion is particularly clear in light of the slim marginal value of the excluded evidence. The trial judge gave Sarfraz substantial leeway to present evidence of a romantic relationship with I.N. The jury heard his testimony that he and I.N. hugged and kissed, watched pornographic videos together, and planned to get married. His friend Azmath Uddin testified that he saw I.N. sitting on Sarfraz's lap and embracing him. Sarfraz's wife testified that she saw the two feeding each other and caught them in bed together. Only the carnal details were excluded.

Given the extensive evidence Sarfraz was allowed to introduce, the incremental impact of the excluded evidence would have been slight. Accordingly, the state supreme court's decision cannot be characterized as an unreasonable application of federal law. The carefully calibrated limitation on Sarfraz's defense was not obviously disproportionate to the purpose the rape-shield law is designed to serve. Habeas relief is unwarranted.

AFFIRMED .