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HAMILTON, Circuit Judge. Illinois prisoner Nicole Harris was convicted in an Illinois state court of murdering her four-year-old son, Jaquari Dancy, and was sentenced to 30 years in prison. It is undisputed that Jaquari died from asphyxiation and that the instrument of death was an elastic band that had come loose from a fitted bed sheet. The parties also agree that Jaquari was not alone when he died. His five-year-old brother Diante was in the top bunk of the bed the two shared. On the day of Jaquari’s death, Harris disciplined the boys for leaving the apartment while she was across the street doing laundry. The State’s theory was that Jaquari would not stop crying, and Harris grew so mad that she strangled him with the elastic band while Diante slept in the bunk above. The defense theory was that Jaquari had wrapped the elastic around his own neck and accidentally asphyxiated himself while Harris was at the laundromat. At trial, by far the most damning evidence against Harris was her videotaped confession, recorded the day after Jaquari’s death following 27 hours of intermittent interrogation at a Chicago police station. In the tape, Harris admitted to choking Jaquari with the elastic band because he had misbehaved. Harris’s best exculpatory evidence was the proffered testimony of Diante, age six at trial, who has maintained since he was first interviewed the day after Jaquari’s death that his brother wrapped the elastic band around his own neck and that neither his mother nor father was present when he did so. The jury never heard Diante’s testimony, however, because the trial court determined that Diante was not a competent witness. No one disputes that the trial judge made a legal error in reaching this conclusion: he reversed Illinois law’s presumption of competency by requiring the defendant, as the proponent of the witness, to prove that Diante was competent to testify. Illinois’s competency statute places the burden of proof on the party challenging competency — in this case, the State — even when the witness is a child. See 725 ILCS 5/115-14(c). In this collateral attack on her conviction, Harris contends that the trial court’s exclusion of Diante’s testimony violated her federal Sixth Amendment right to present witnesses in her own defense, see Washington v. Texas, 388 U.S. 14, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967), and that she received ineffective assistance of counsel at Diante’s competency hearing. The original state trial court denied Harris’s motion for a new trial on these and other grounds. The Illinois Appellate Court rejected her direct appeal, and the district court determined that federal habeas relief was not available. We reverse with instructions to grant the writ. A court’s exclusion of defense evidence violates the Compulsory Process Clause of the Sixth Amendment where the evidence is material to the outcome of trial and the application of the evidentiary exclusion is arbitrary or disproportionate to the state’s legitimate interests promoted by the rule. Although Diante and his testimony posed challenges, the complete exclusion of this critical exculpatory evidence in this case was arbitrary and disproportionate to the truth-seeking and reliability concerns advanced by witness competency restrictions. We review this issue de novo because it was not addressed by the Illinois courts. The disqualification of Diante as a witness violated Harris’s Sixth Amendment right to present a complete defense. We also conclude that trial counsel’s serious errors in the competency hearing deprived Harris of the right to effective counsel. As the only eyewitness to Jaquari’s death, Diante’s testimony was essential to Harris’s defense. His competency hearing was crucial, but Harris’s counsel was not ready for it: he did not interview Diante, he did not secure the presence of a witness who would have shown that Diante’s recollections of what happened were consistent and credible, and he did not correct the trial court’s misapplication of the burden of proof. Under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), and its progeny, each of these mistakes— lack of investigation, failure to secure a key witness, and ignorance of applicable law — amounted to constitutionally deficient performance of defense counsel. If counsel had taken simple and obvious steps to prepare for the hearing, it is reasonably likely that Diante would have been deemed competent. And if the jury had heard his testimony, there is a reasonable probability that the outcome of the trial would have been different. In concluding that Harris was not prejudiced by her counsel’s errors at the competency hearing, the state appellate court unreasonably applied Strickland. I. Factual and Procedural Background The underlying facts of this case are detailed in the Illinois Appellate Court’s decision affirming Harris’s conviction and sentence. People v. Harris, 389 Ill.App.3d 107, 328 Ill.Dec. 567, 904 N.E.2d 1077 (2009). Those facts are entitled to a presumption of accuracy, see 28 U.S.C. § 2254(e)(1), and they are in any event uncontested insofar as they are relevant to our decision. A. Jaquari’s Death and the Initial Investigation In May 2005, Harris, age 23, lived in an apartment on Chicago’s west side with her boyfriend, Sta-Von Dancy, and their two sons, fíve-year-old Diante and four-year-old Jaquari. In the afternoon of Saturday, May 14, Harris and Dancy went to the laundromat across the street, leaving their sons home alone for approximately 40 minutes with instructions to stay in the apartment. While the clothes were drying, Harris returned home and discovered Di-ante in the hallway and Jaquari playing outside. Harris yelled at the children and ordered them to their bedroom, where Jaquari began crying. At this point, Dancy returned to the apartment, spoke to his children in them room, and lay down to take a nap. When he awakened, Dancy discovered Jaquari lying on the floor of the boys’ bedroom, unresponsive and blue in the face. An elastic band hanging from Di-ante’s fitted sheet was wrapped repeatedly (close to ten times) around Jaquari’s neck. Dancy unwrapped the band and performed mouth-to-mouth resuscitation. Jaquari remained unconscious. Dancy lifted him up and ran outside, where he met Harris returning again from the laundromat. The two jumped in their car and raced off in search of a hospital with Harris driving and Dancy continuing CPR on Jaquari in the back seat. They called 911 and eventually met an ambulance that took Jaquari to a hospital. Harris and Dancy returned home to retrieve Diante and then went to the hospital, where Jaquari was pronounced dead. Chicago police officers arrived at the hospital to begin their investigation into Jaquari’s death. After a brief conversation with detectives around 7:15 p.m., Harris and Dancy agreed to accompany them to the police station to answer further questions. Detectives interviewed the parents in separate rooms. With Diante on her lap, Harris answered questions for approximately 30 minutes before the detectives left to continue their investigation at the scene. Around midnight, Diante was taken to his grandmother’s home by an official with the Department of Child and Family Services. Back at the family’s apartment, officers ordered crime scene technicians to collect the sheet with the loose elastic band and a telephone cord they suspected might have been used to strangle Jaquari. After speaking with other tenants in the building, the detectives returned to the station to confront Harris with discrepancies between her earlier account and what they had learned from her neighbors, who said she had struck her children with a belt that day. According to the detectives, after approximately fifteen minutes of questioning, Harris broke down, started crying, and spontaneously admitted, “I wrapped the phone cord around Jaquari’s neck and then I wrapped the elastic band from the bed sheet around his neck to make it look like an accident.” Harris, 328 Ill.Dec. 567, 904 N.E.2d at 1080. That first confession was undisputedly false: the autopsy would later show that the telephone cord played no role in Jaquari’s death. The detectives read Harris her Miranda rights, which she said she understood. Over the next 24 hours, Harris recanted her initial unwarned confession, slept overnight in a holding cell, took a polygraph examination (with inconclusive results), and confessed a second time — this time saying she had used the elastic band, which conformed to the physical evidence. A prosecutor arrived and obtained a videotaped statement of Harris’s confession. In it, Harris stated that she had struck Jaquari with a belt when she came over from the laundromat and that because he would not stop crying, she wrapped the sheet’s elastic band around his neck until she saw blood coming from his nose. She said she then left the room, attempted to fix a phone jack, and returned to the laundromat to retrieve her .clothing. She was charged with first-degree murder. Her trial began on October 20, 2005 in Cook County Circuit Court. B. The Trial At trial, Harris’s videotaped confession provided the State’s most powerful evidence against her. - Several police officers and prosecutors testified for the prosecution to discuss the investigation and interrogation of Harris. Dancy was called by both the State and the defense. He testified that when he found Jaquari lying inert on the floor, he saw a clear mucus bubble coming out of the boy’s nose. Dancy said he had seen the elastic band before, hanging from Diante’s sheet on the top bunk down almost to the bottom bed. Dancy also testified that, on previous occasions, Jaquari had played with the elastic by wrapping it around his neck. According to Dancy, Diante was in the room lying on his top bunk bed when he found Jaquari. The State also called Dr. John Scott Denton, who had conducted the postmortem examination. Dr. Denton found impression or ligature marks on Jaquari’s neck that were an “exact fit” to the blue sheet’s elastic band. His report indicated that the impression marks did not match the telephone cord that had initially aroused the police’s suspicions and which Harris had identified as the murder weapon in her first, “spontaneous” confession. Dr. Denton also acknowledged that he had at first concluded after the May 15 autopsy that Jaquari’s death was accidental — specifically, that Jaquari had “become entangled with an elastic bed fitted sheet and had fallen to the ground from his upper bunk.” Harris, 328 Ill.Dec. 567, 904 N.E.2d at 1083. Several days later, however, a detective told Dr. Denton that Harris had confessed to strangling Jaquari. Dr. Denton also learned from the investigation report that Jaquari slept on the bottom bunk and that traces of blood were found on the lower bed’s linen. Dr. Den-ton then revised his medical opinion to conclude that Jaquari’s death was a homicide. Dr. Denton did not say whether he was also told that Diante had been present when Jaquari died and said he saw Jaquari wrap the elastic around his own neck. Harris testified in her own defense. She testified that when she came home from the laundromat to find her children outside the apartment, she scolded them and sent them to their room but did not strike them. She then fiddled with a telephone jack, helped Dancy to the bedroom to take a nap, and went across the street to get her clothes from the dryer. Upon her return to the apartment, she was met by Dancy outside bearing Jaquari in his arms. This testimony obviously contradicted the videotaped confession the jury had already seen. But Harris told the jury that the videotaped confession was the product of a 27-hour coercive interrogation in which detectives pushed her, deprived her of food and water, threatened her, and promised her lenient treatment in exchange for cooperation. In the videotaped confession, though, she had said that the police had fed her and treated her well and had made neither threats nor promises. The defense theory of accidental death was supported by Dancy, who had previously seen Jaquari coiling the sheet’s elastic band around his neck, and by other family members who spoke more generally about his curiosity and playfulness. For example, one aunt said that she had once seen Jaquari put a plastic laundry bag over his face. The defense’s key witness, however, was six-year-old Diante, who was with Jaquari when he died. The day after Jaquari’s death, Diante was interviewed by Ale Levy, an investigator with the Child Advocacy Center, an agency that partners with the Chicago Police Department, the State’s Attorney, and the Department of Child and Family Services. A Chicago police detective who was present for Levy’s interview took notes. The notes state that Diante “knows his age,” “his colors,” “different amounts,” his “grade in school,” and the “difference between truth/lies.” Di-ante indicated that he “knows about Jaquari’s death, knows Jaquari was at the hospital.” Diante also said that Jaquari had “wanted to go outside” but he “got in trouble.” “Mom and Dad came home [and] gave both of them a spanking. Mom spanked Diante with Belt on his leg,” which “was bleeding.” Most important, Diante said that “Jaquari was playing [and] wrapped elastic around neck from blue sheet” and that Diante was “playing Spiderman game” and “couldn’t help Jaquari get out of his sheet.” Levy wrote, “Diante & Jaquari were supposed to go to sleep.” Towards the end, Jaquari told Levy, “ ‘Jaquari had a bubble’ while he was asleep.” He said, “Jaquari died it happened in their bedroom” and “Diante was sleeping when Jaquari died.” C. The Competency Hearing and Ruling Although Diante was also listed as a witness for the State, the State moved to disqualify him as incompetent to testify. Under Illinois law, every person is presumed competent to be a witness and will be permitted to testify unless he or she is either (1) “Incapable of expressing himself or herself concerning the matter so as to be understood, either directly or through interpretation by one who can understand him or her”; or (2) “Incapable of understanding the duty of a witness to tell the truth.” 725 ILCS 5/115 — 14(a), (b); see People v. Velasco, 216 Ill.App.3d 578, 159 Ill.Dec. 147, 575 N.E.2d 954, 959 (1991). The burden of proof is on the party challenging competency. See 725 ILCS 5/115—14(c); People v. Hoke, 213 Ill.App.3d 263, 157 Ill.Dec. 124, 571 N.E.2d 1143, 1148 (1991). The trial court began the competency hearing with a basic legal error, stating “the Defense, it’s their witness whom they’re attempting to call. They shall bear the burden of proof in demonstrating Di-ante’s competency.” No objection was made. With defense counsel’s agreement, the hearing took place without Harris present. Diante took the stand and fielded some preliminary questions from defense counsel, spelling his name and stating his age, birthday, the cities where he had lived, his teacher’s name, and the colors of certain objects. Asked by the court if he knew the difference between a truth and a lie, Diante responded, “Telling a lie, you might get in trouble. Telling the truth, you might get a star,” which he agreed was “a good thing.” Diante also described the events from the day Jaquari died. On the last day that Diante had been in his room at the North Chicago apartment, he had been with Jaquari and was “Playing my game.” Defense counsel asked what Jaquari was doing and Diante replied, “Jaquari was playing with that string and wrapping it around his neck.” S.A. 118. Asked what string he was referring to, Diante said it was the band from the blue sheet. He also testified that no one else was in the room with them when Jaquari was wrapping the sheet’s elastic around his neck. The prosecutor later asked whether Jaquari “wrapped something around his neck from the sheet.” Diante nodded and said that the sheet was “On my bed” and that Jaquari was “Standing on the floor” while Diante was “Sitting, playing with my toys.” S.A. 125. The prosecutor also asked Diante if he remembered telling a Department of Child and Family Services investigator named Karen Wilson — who spoke with Diante the day after Levy did — that he was asleep when Jaquari “got hurt.” Diante answered yes. S.A. 127. In his direct questioning, defense counsel had asked Diante whether he knew “the difference between real people and cartoons.” S.A. 118. Diante said he did and named “Scooby-Doo, Tom and Jerry” as examples of the latter. S.A. 119. Later, the prosecutor followed up on this line of questioning, but after referring to the original difference between real people and cartoons, the prosecutor shifted to use the word “real” differently to ask about the difference between real people and fictional characters. This shift caused some confusion: Q Okay. Now, you were talking about some cartoons a couple of minutes ago. You were talking about Scooby-Doo, and cartoons and real things, right? A (Nodding.) Q Do you think Spiderman is real? A Yes. Q And have you ever seen Spiderman in person? A Yes. Q Okay. And what did you say to Spiderman when you saw him in person? A Nothing. Q You didn’t say anything to him? A (Nodding.) Q Have you ever seen Scooby-Doo? A No. Q Okay. Is Scooby-Doo real? A No. Q Okay. Scooby-Doo is what? A A movie. Q Okay. And how about The Hulk? Is The Hulk real or is he something else? A Something else. Q Okay. Let’s see. How about Santa Claus, is Santa Claus real? A Yes. Q And have you ever seen Santa Claus in person? A No. S.A. 122-23. Later, the prosecutor asked whether Diante believed the tooth fairy was real, to which he said yes. S.A. 129. Consistent with the real-versus-eartoon framework established by the defense, Di-ante evidently understood the prosecutor to be asking whether Spiderman and Santa Claus were animated or human characters, and that they were “real” insofar as they were not cartoons, which was correct. See, e.g., Elf (New Line Cinema 2003) (live-action film); Spider-Man (Columbia Pictures 2002) (same). At trial, Dancy testified that Diante was familiar with the recent Spiderman live-action films at the time of Jaquari’s death. The prosecutor asked Diante about Jaquari, and once again ambiguous questioning and a failure to follow up generated confusion: Q .... You told me earlier that you have seen Jaquari in heaven, right? A Yes. Q And do you remember the last time you saw Jaquari in heaven? A Where I was in the rainbow. Q When you were in the what? A In the rainbow. Q “In the rainbow”? You were in the rainbow? A Uhn-uhn. No, in the car. Q Oh, in the car. And you saw Jaquari in heaven then? A (Nodding.) S.A. 123-24. The transcript reads, “rainbow,” but the context shows that Di-ante was saying “limo.” That was the conclusion of Dr. Robert Galatzer-Levy, a child psychiatrist who conducted a thorough competency assessment of Diante six months after trial. See S.A. 141. (“[H]is pronunciation of the word ‘limo’ was difficult for this evaluator to understand; I initially believed he was saying something like ‘lambo.’ ”). As for the “heaven” reference, during Dr. Galatzer-Levy’s evaluation, Diante described a church as a “church with heaven” and a courtroom as a “church with the judge.” Id. That would be consistent with the rest of Diante’s testimony on the subject at the competency hearing, in which he said that other living family members were present “in heaven” in an exchange that took on great importance for the judge: Q Who else was in heaven with him? A My brother and my cousin. Q Okay. What’s your brother’s name? A Junior. Q Okay. And he was there, too? A (Nodding.) Q And did you talk to Jaquari then? A Uh-huh. Q Did he say anything to you? A Yes. Q What did he say to you? A He-He said, my mommy killed my brother, and my mommy didn’t. Q Okay. Now, I want to ask you a little bit about your bedroom.... S.A. 124-25. Because this account involves both of Diante’s brothers, we cannot be completely certain whether the “He” in the penultimate line refers to Junior or to Jaquari. The difference bears on both the competency determination and Harris’s guilt or innocence. If the speaker was Junior, Diante was describing what his surviving brother Junior had told him at the wake or funeral: Junior said that Harris had killed Jaquari, and Diante was telling the judge that was wrong. The testimony is entirely different if Diante meant that Jaquari appeared to his brothers from beyond the grave to accuse their mother of killing him. The first reading is supported by the fact that Diante said, “He said, my mommy killed my brother,” not “He said, my mommy killed me,” or “He said, my mommy killed him.” The best support for the second reading is that Jaquari was the brother the prosecutor had last mentioned (three questions earlier), but it’s safe to say that six-year-old Diante was not precise with pronouns and antecedents. Given the ambiguity, one would have expected counsel or the court to ask some follow-up questions to learn what Diante meant, at least before assuming that he was reporting a visit from beyond the grave. But nothing more was said on the subject. And not only did the court assume that this testimony referred to a communication with Jaquari’s spirit, but it relied heavily on his report of this supposed “fantasy” to find that Diante was not competent to testify. At the close of Diante’s testimony, the court asked him: “did you — anyone tell you what you should say here when you got to court?” Diante said “No.” “Have you spoken before with any of the people who are here today before you came to court?” Diante again answered “No.” S.A. 131. Then, the following final exchange took place between the judge and Diante: Q Diante, you [told] me you remember playing Spiderman in your bedroom with your brother, is that right? A Yes. Q Do you remember anything else that happened that day? A No. Q Nothing at all? A No. Q Okay. Anything further, Mr. Wright? S.A. 132. Following Diante’s testimony, defense counsel said that he wished to call Ale Levy, the investigator who interviewed Di-ante the day after his brother’s death. Levy was not present at the courthouse, however. Defense counsel said that he had subpoenaed Levy, but neither the court nor the prosecutor was familiar with her. The court asked, “have you made any effort to procure her appearance here at this time, so as not to delay these proceedings?” Dkt. No. 1-17 at 81. Defense counsel said he had not. In response to the court’s question about the substance of Levy’s expected testimony, defense counsel said that she “actually interviewed Diante Dancy; and asked him a lot of the same questions that was asked,” and “he was able to tell her, on that day, which is roughly 12, 15 hours after the event, exactly everything that happened.” Id. at 82. The trial judge replied, “I’m not saying it’s not relevant. I’m just at a lack to find out what that would be, in order to determine whether I would grant a continuance to get that witness here.” Id. at 83. Counsel then said the defense had no further witnesses. The court confirmed that counsel was “not choosing to call that person at this time?” Counsel answered no. The State then called Karen Wilson, the second investigator to interview Diante after Jaquari died. She testified that in her conversation with Diante, he stated that Scooby-Doo, Spiderman, and Santa Claus were real persons. Dkt. No. 1-17 at 86. She also said that Diante told her he was asleep when his brother got hurt. On cross-examination, Wilson agreed that Di-ante had said he did not see “mommy or daddy tie a sheet around Jaquari’s neck.” Dkt. 1-17 at 89. The court heard oral argument. Defense counsel went first, contending that Jaquari really was in heaven, and that it was perfectly reasonable for a six-year-old to believe in Santa Claus and the tooth fairy, and that such beliefs did not affect his “ability to recall the facts on May 14th.” Dkt. No. 1-17 at 98. Counsel concluded by saying “we believe that we’ve met our burden” showing that Diante was competent to testify. Id. at 100. The prosecutor argued that Diante was incompetent because of his “inability to differentiate between reality and fantasy with the Spiderman, Santa Claus, tooth fairy characters,” and that he testified not just that he believed his brother was in heaven but that he “saw his brother in heaven.” Id. at 101 (emphasis added). In rebuttal, defense counsel stated: “The only issue is that ... he observed on that day Jaquari wrap the sheet around his own neck. He knew where they were at, he knew who was present. That’s the only issue that is relevant as relates to the information for him being called as a witness.” Id. at 102. The court ruled that Diante was incompetent. The judge began by saying: “Defense counsel misperceives what the issue is with regard to witness competency” because “a two month old baby could have been in the room and witnessed or observed what occurred, but that would not make them a competent witness if they’re lacking other criteria.” He acknowledged that Illinois had abolished age-based presumptions of incompetency and that the statute now provided for only two bases for disqualification: (1) inability to express oneself so as to be understood; or (2) inability to understand the duty of a witness to tell the truth. S.A. 85-86; see 725 ILCS 5/115-14. The court first addressed the second prong, saying: “I don’t find any questions at all that were posed to the witness with regard to his understanding of any concept of a duty to tell the truth when presented in a courtroom.” S.A. 87. Diante’s testimony that “[y]ou get in trouble” for telling a lie and “[y]ou get a star” for telling a truth “gave the Court very little insight into whether or not Diante knows what is the truth and what is a lie or not true.” S.A. 86. “The witness was never asked whether he would promise to tell the truth and what that might mean to him here in this proceeding.” S.A. 88. Turning to the first prong, the court said it had “considerable question as to that issue,” identifying a number of factors that cast doubt on Diante’s ability to “perceive and remember events and to relate them.” S.A. 88. First, Diante recalled “playing Spiderman” and “the aspect with the cord and the neck,” but the court, referring to its own question at the end of his testimony, said Diante “remembers nothing else at all from that day.” Id. Second, the court questioned whether Diante had the ability to distinguish between reality and fantasy: Diante is still at that point in his life ... where the Court cannot say that he has moved through that youthful period or childhood period of fantasy with regard to still believing certain things to be real, whether it be Spiderman, who he says, he has met in person, the tooth fairy, Santa Claus.... He said, he met with his brother in heaven and his brother told him his mother killed him. I mean, that is not real. That is a fantasy. S.A. 89-90. The court then concluded that Diante was incompetent to testify under either prong of the statute: And so I do believe at this point in time Diante lacks the ability to differentiate between reality and fantasy. And also, I believe he lacks the ability to recall the events of the date in question and to be able to communicate them effectively here in court under an understanding and acceptance of a duty to testify truthfully in this case. And again, it is not clear to this Court that even he understands to differentiate significantly between those two concepts, truthfulness and falsehood. S.A. 90. Diante did not testify. The jury convicted Harris of first-degree murder. D. Post-Conviction Proceedings With new counsel, Harris moved for a new trial. Her supplemental motion included four constitutional claims: (1) the court violated Harris’s right to call witnesses in her own defense in deeming Di-ante incompetent to testify (Sixth Amendment right to compulsory process); (2) the evidence was insufficient to prove the corpus delicti element of murder (Due Process); (3) the court erred in denying her motion to suppress her confession (Fifth Amendment right against self-incrimination); and (4) trial counsel was ineffective (Sixth Amendment right to counsel). Her motion included Dr. Galatzer-Levy’s competency assessment. He had concluded that Diante was “neither incapable of expressing himself concerning the events surrounding his brother’s death, nor incapable of understanding the duty of a witness to tell the truth.” S.A. 143. Harris also submitted the interview notes of Child Advocacy Center investigator Ale Levy and affidavits from two expert witnesses on false confessions and pediatric asphyxiation. The trial court denied Harris’s motion for a new trial. In addressing the issue of Diante’s competency hearing, the court conceded that it had erred in placing the burden of proof on Harris but held that it would have reached the same result even if the State had borne the burden. In his ruling from the bench, the trial judge said: “It was clear to the Court that [Diante] was in the world of a child. That he could not do those things that the law requires competent witnesses to do, so that was upon that basis that I found [Diante] not competent to testify, and that would have been the outcome or my finding regardless of whether I had articulated the correct burden of proof.” S.A. 59. Aside from this vague, post hoc justification for its ruling and some recitation of the statutory language, the court did not elaborate on its ruling at trial that Diante was incompetent to testify. The trial court did not address Harris’s Compulsory Process claim. The court sentenced Harris to 30 years in prison. On direct appeal, the Illinois Appellate Court affirmed. People v. Harris, 389 Ill. App.3d 107, 328 Ill.Dec. 567, 904 N.E.2d 1077 (2009). The panel majority held that: (1) the trial court did not abuse its discretion in finding Diante incompetent under Illinois’s witness competency statute and that, even if it had, any error was harmless because Diante’s testimony would not have influenced the verdict; (2) Dr. Denton’s revised conclusion that Jaquari’s death was a homicide was sufficiently independent to establish that a crime had occurred; (3) the motion to suppress was properly denied because Harris was not in custody during her initial, unwarned confession; and (4) Harris failed to establish an ineffective assistance of counsel claim because “she suffered no prejudice from her counsel’s purported deficiencies.” Id., 328 Ill. Dec. 567, 904 N.E.2d at 1098. One judge dissented, taking the view that Harris’s confession should have been suppressed. Id., 328 Ill.Dec. 567, 904 N.E.2d at 1100-02 (Tully, J., dissenting). Neither the majority nor the dissent said anything about Harris’s Compulsory Process claim. The Supreme Court of Illinois denied Harris’s petition for leave to appeal. Harris filed a petition for habeas corpus under 28 U.S.C. § 2254, seeking relief on the same grounds she presented to the state courts. With the exception of the competency issue, the district court found reasonable the Illinois Appellate Court’s adjudication of each of Harris’s four claims. See Harris v. Thompson, No. 10 cv 6257, 2011 WL 6257143 (N.D.I11. Dec. 14, 2011). As to the incompetency determination, the district court did not recognize that the state courts had neglected to reach Harris’s Compulsory Process claim. Instead, it appears to have treated the state courts’ denial of Harris’s state evidentiary law claims as an adjudication of her Sixth Amendment claim, as well. The district court concluded that the appellate court unreasonably affirmed the trial judge on the basis of the competency statute’s second prong (incomprehension of the duty to tell the truth), since the trial judge had said that he had heard no testimony on that question, and it was the State that bore the burden of proof. However, the appellate court had also affirmed the incompetency determination on the grounds of the first prong (inability to be understood), and the district court concluded that this ground for affirmance was reasonable because there was some evidence on that issue. The district court also found reasonable the appellate court’s conclusion that any error in disallowing Diante’s testimony was harmless, and the court denied the petition for a writ of habeas corpus. Harris timely appealed. The parties agree that she has exhausted her state remedies and no procedural bar applies to any of the claims presented. II. Habeas Corpus Review Under 28 U.S.C. § 2251 We have jurisdiction under 28 U.S.C. § 2253(a), and we review de novo the district court’s denial of habeas corpus relief. See Steffes v. Pollard, 663 F.3d 276, 281 (7th Cir.2011). The statutory authority of federal courts to issue a habeas writ for persons in state custody is § 2254, as amended by the Antiterrorism and Effective Death Penalty Act (AEDPA). Under AEDPA, a habeas petition may be granted only if a state court’s ruling on a federal constitutional question “was contrary to, or involved an unreasonable application of, clearly established Federal law,” or “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d)(1) & (2). In applying this “difficult to meet ... and highly deferential standard,” Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011) (internal quotation marks omitted), federal courts must avoid “using federal habeas corpus review as a vehicle to second-guess the reasonable decisions of state courts.” Parker v. Matthews, — U.S. -, 132 S.Ct. 2148, 2149, 183 L.Ed.2d 32 (2012), quoting Renico v. Lett, — U.S. -, 130 S.Ct. 1855, 1866, 176 L.Ed.2d 678 (2010). Rather, “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.” Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 786-87, 178 L.Ed.2d 624 (2011). Our review under § 2254(d) “is limited to the record that was before the state court.” Pinholster, 131 S.Ct. at 1398. AEDPA’s deferential standard of review applies only to claims that were actually “adjudicated on the merits in State court proceedings.” 28 U.S.C. § 2254(d). Where the state courts did not reach a federal constitutional issue, “the claim is reviewed de novo.” Cone v. Bell, 556 U.S. 449, 472, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009). When no state court has squarely addressed the merits of a habeas claim, “we review the claim under the pre-AEDPA standard of 28 U.S.C. § 2243, under which we ‘dispose of the matter as law and justice require.’ ” Toliver v. Pollard, 688 F.3d 853, 859 (7th Cir.2012), quoting Morales v. Johnson, 659 F.3d 588, 599 (7th Cir.2011). The operative decision under review is that of the last state court to address a given claim on the merits. See Greene v. Fisher, — U.S. -, 132 S.Ct. 38, 45, 181 L.Ed.2d 336 (2011); Garth v. Davis, 470 F.3d 702, 710 (7th Cir.2006). In this case, that is the Illinois Appellate Court’s decision in People v. Harris, 389 Ill.App.3d 107, 328 Ill. Dec. 567, 904 N.E.2d 1077 (2009). III. Compulsory Process Clause Claim A. Standard of Review The Sixth Amendment guarantees the accused the right to “have compulsory process for obtaining witnesses in his favor.” As a threshold matter, we must determine whether AEDPA deference applies to this claim. The habeas petitioner clearly presented a federal constitutional claim to the state courts, which affirmed her conviction in a published opinion but did not explicitly address or even acknowledge the existence of the federal constitutional issue. In her brief to the state court, Harris alleged a deprivation of “her right to compulsory process under the Sixth Amendment of the U.S. Constitution and Article I, § 8 of the Illinois Constitution,” cited the foundational Supreme Court case, Washington v. Texas, 388 U.S. 14, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967), and other federal and state cases, and set forth the applicable constitutional standard. See Dkt. No. 1-5 at 42. Yet the state court analyzed the disqualification of Diante as a witness purely as an issue of state evidentiary law, reviewing the trial court’s incompetency determination for an abuse of discretion and harmless error. See 328 Ill.Dec. 567, 904 N.E.2d at 1091-95. At the beginning of the relevant section of its opinion, the court acknowledged that Harris “asserted] that the trial court abused its discretion and violated her constitutional rights when it ruled that Diante Dancy was incompetent to testify.” Id., 328 Ill. Dec. 567, 904 N.E.2d at 1091-92 (emphasis added). But the appellate court never identified which constitutional rights were at issue or referred to the Compulsory Process Clause, the Sixth Amendment, or even the Due Process Clause. And the court cited no case — state or federal — on the constitutional issue. The appellate court’s silence on the issue fell below even the low threshold a state court decision must meet to qualify as “on the merits” under AEDPA. The state court need not explain its reasoning in rejecting the petitioner’s federal claim. See Richter, 131 S.Ct. at 784; see also Muth v. Frank, 412 F.3d 808, 815 (7th Cir.2005) (“AEDPA’s requirement that a petitioner’s claim be adjudicated on the merits by a state court is not an entitlement to a well-articulated or even a correct decision by a state court.”). Nor must it cite or even be aware of any particular cases. See Richter, 131 S.Ct. at 784. Sometimes even saying nothing at all will suffice. In Richter, the Supreme Court held that the California Supreme Court’s one-sentence summary order denying a prisoner’s petition for state collateral relief was “on the merits” for AEDPA purposes: “When a federal claim has been presented to a state court and the state court has denied relief, it may be presumed that the state court adjudicated the claim on the merits in the absence of any indication or state-law procedural principles to the contrary.” 131 S.Ct. at 784-85. But that “presumption may be overcome when there is reason to think some other explanation for the state court’s decision is more likely,” though there was no such reason in Richter. Id. at 785. Although the state supreme court’s summary dismissal of post-conviction relief in Richter did not address the merits of the petitioner’s federal constitutional arguments, “the state court did not say it was denying the claim for any other reason,” such as a procedural default or other independent and adequate state-law ground. Id. at 784. In this case, by contrast, we have ample reason to think some other explanation for the state court’s decision is more likely — the very reasons the state court actually gave, which were all based on state evidence law, not federal constitutional law. The state court’s decision on the incompetency ruling reached four legal conclusions. First, the trial court’s “procedural error” in misallocating of the burden of proof was not “outcome-determinative” in the ultimate determination of incompetency. Harris, 328 Ill.Dec. 567, 904 N.E.2d at 1092. Second, the trial court did not “base[ ] its analysis on factors outside Illinois statutory law.” Id., 328 Ill. Dec. 567, 904 N.E.2d at 1093. Third, the trial court’s “determination of incompetency” was not “unsupported by the record.” Id., 328 IlLDec. 567, 904 N.E.2d at 1094. Finally, even assuming that the trial court had erred in its ruling, the error had been “harmless beyond a reasonable doubt.” Id., 328 Ill.Dec. 567, 904 N.E.2d at 1094. In sum, the appellate court’s adjudication rested entirely on Harris’s claim of state evidentiary error. It did not hint at any federal (or state) constitutional ground of decision. The Richter presumption and AEDPA deference therefore do not apply. See Sussman v. Jenkins, 642 F.3d 532, 534 (7th Cir.2011) (Ripple, J., in chambers) (denying motion to stay mandate and concluding that Richter presumption was inapplicable where state appellate court issued an opinion but did not address the constitutional question); see also Sussman v. Jenkins, 636 F.3d 329, 350 (7th Cir.2011) (underlying opinion). This also is not a case where an earlier state opinion- “fairly appear[s] to rest primarily upon federal law,” but a later one is silent or cryptic. See Ylst v. Nunnemaker, 501 U.S. 797, 803, 111 S.Ct. 2590, 115 L.Ed.2d 706 (1991), quoting Coleman v. Thompson, 501 U.S. 722, 740, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). In that situation, the federal habeas court “ ‘looks through’ [the later decision] to the last reasoned decision” and treats the later one as reaching the merits if the earlier one did. Ylst, 501 U.S. at 805, 111 S.Ct. 2590. In this case neither the state appellate court nor trial court mentioned Harris’s compulsory process claim. When we look for the “last explained state-court judgment” on Harris’s Sixth Amendment right to present a defense, we do not find one. No state court has actually decided it. It follows from the Supreme Court’s AEDPA jurisprudence that where a state court overlooks a constitutional claim that was fairly presented to it, federal review is de novo. In Cone v. Bell, 556 U.S. 449, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009), the state post-conviction court deliberately bypassed a federal claim because it believed — erroneously—that the state courts had already addressed it on direct appeal. Because the state courts therefore never reached the merits of the Brady claim, the Supreme Court reviewed the issue de novo. Id. at 472, 129 S.Ct. 1769. Cone shows that when the state court knowingly (but mistakenly) declines to address a constitutional claim, AEDPA deference does not apply. It would be odd, then, if AED-PA deference did apply when the state court’s decision simply overlooked the constitutional issue, as happened here. This case is also analogous to the relatively common situation in which the state courts address one prong of the two-prong Strickland v. Washington test for ineffective assistance of counsel, but not the other. In that situation, federal courts apply AEDPA deference to the prong the state courts reached but review the unaddressed prong de novo. E.g., Rompilla v. Beard, 545 U.S. 374, 390, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005) {de novo review where state courts did not reach prejudice prong); Wiggins v. Smith, 539 U.S. 510, 534, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (same); see also Sussman, 636 F.3d at 350 (applying Rompilla/Wiggins rule after Richter); accord, Toliver v. Pollard, 688 F.3d 853, 857 (7th Cir.2012) (same); Hooks v. Workman, 689 F.3d 1148, 1188 (10th Cir.2012) (same); Foster v. Wolfenbarger, 687 F.3d 702, 709 (6th Cir.2012) (same); Johnson v. Sec’y, DOC, 643 F.3d 907, 930 (11th Cir.2011). Here, the state courts simply have not addressed the federal constitutional issue. When that happens, federal habeas review must be de novo for there is no state court judgment to which we could defer. See, e.g., Fenenbock v. Dir. of Corrections, 681 F.3d 968, 978 n. 12 (9th Cir.2012) (“No deference is due to the last reasoned state court opinion because it failed to address the constitutional question, resolving the claim only on state evidentiary grounds.”); accord, Campbell v. Bradshaw, 674 F.3d 578, 596 (6th Cir.2012), petition for cert. filed (U.S. July 18, 2012) (No. 12-5374); Han Tak Lee v. Glunt, 667 F.3d 397, 403 (3d Cir.2012); Clements v. Clarke, 592 F.3d 45, 55 (1st Cir.2010). AEDPA requires federal courts to accord substantial deference to state court adjudications of federal constitutional claims. Such deference is “part of the basic structure of federal habeas jurisdiction,” which is “designed to confirm that state courts are the principal forum for asserting constitutional challenges to state convictions” and to honor “the State’s significant interest in repose for concluded litigation.” Richter, 131 S.Ct. at 787, quoting Harris v. Reed, 489 U.S. 255, 282, 109 S.Ct. 1038, 103 L.Ed.2d 308 (1989) (Kennedy, J., dissenting). Where the state courts have overlooked a constitutional claim, however, these comity and finality concerns have less force. In the absence of a state decision on the merits, our review is “not circumscribed by a state court conclusion” on the issue. Wiggins, 539 U.S. at 534,123 S.Ct. 2527. The Illinois courts did not adjudicate Harris’s Compulsory Process Clause claim “on the merits,” so our review is de novo. B. The Constitutional Standard The Compulsory Process Clause, which provides that the accused shall have the right “to have compulsory process for obtaining witnesses in his favor,” together with the Due Process Clause of the Fourteenth Amendment, embodies a substantive right to present a meaningful and complete criminal defense. See Holmes v. South Carolina, 547 U.S. 319, 324, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006); Taylor v. Illinois, 484 U.S. 400, 408, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988). “The right to offer the testimony of witnesses, and to compel their attendance, ... is in plain terms the right to present a defense, the right to present the defendant’s version of the facts as well as the prosecution’s to the jury so it may decide where the truth lies.” Washington v. Texas, 388 U.S. 14, 19, 87 5.Ct. 1920, 18 L.Ed.2d 1019 (1967). “Few rights are more fundamental than that of an accused to present witnesses in his own defense,” Taylor, 484 U.S. at 408,108 S.Ct. 646 — a right Chief Justice Marshall described as “sacred.” United States v. Burr, 25 F.Cas. 30, 33 (C.C.D.Va.1807). The compulsory process right is an “essential attribute of the adversary system itself,” Taylor, 484 U.S. at 408, 108 S.Ct. 646, and “imperative to the function of the courts,” which “depend on full disclosure of all the facts, within the framework of the rules of evidence.” United States v. Nixon, 418 U.S. 683, 709, 94 S.Ct. 3090, 41 L.Ed.2d 1039 (1974). Of course, the right is not unlimited. The defendant “must comply with established rules of procedure and evidence designed to assure both fairness and reliability.” Chambers v. Mississippi 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). The accused “does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence.” Taylor, 484 U.S. at 410, 108 S.Ct. 646. While a “trial court may not ignore the fundamental character of the defendant’s right to offer the testimony of witnesses in his favor,” the “countervailing public interest[ ]” in the “integrity of the adversary process, which depends both on the presentation of reliable evidence and rejection of unreliable evidence, ... must also weigh in the balance.” Id. at 414, 415, 108 S.Ct. 646. Thus, the Compulsory Process Clause does not require criminal courts to admit evidence that is irrelevant, Crane v. Kentucky, 476 U.S. 683, 689-90, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986), testimony by persons who are mentally infirm, see Washington, 388 U.S. at 23 n. 21, 87 S.Ct. 1920, or evidence that represents a half-truth, see United States v. Nobles, 422 U.S. 225, 241, 95 S.Ct. 2160, 45 L.Ed.2d 141 (1975). On the other hand, the exclusion of defense evidence “abridge[s] an accused’s right to present a defense” where the restriction is “ ‘arbitrary’ or ‘disproportionate to the purposes’ [it is] designed to serve,” and the evidence “implicate[s] a sufficiently weighty interest of the accused.” United States v. Scheffer, 523 U.S. 303, 308-09, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998), quoting Rock v. Arkansas, 483 U.S. 44, 56, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987). For example, the Supreme Court has struck down under the Compulsory Process Clause a rule against introducing the testimony of an alleged accomplice, Washington, 388 U.S. at 22-23, 87 S.Ct. 1920; an application of the hearsay bar to statements that “were originally made and subsequently offered at trial under circumstances that provided considerable assurance of their reliability,” Chambers, 410 U.S. at 300, 93 S.Ct. 1038; the exclusion of evidence bearing on the credibility of a voluntary confession, Crane, 476 U.S. at 688-91, 106 S.Ct. 2142; and a per se rule excluding all post-hypnosis testimony, Rock, 483 U.S. at 56-62, 107 S.Ct. 2704. The Court has acknowledged the “power of States to exclude evidence through the application of evidentiary rules that themselves serve the interests of fairness and reliability — even if the defendant would prefer to see that evidence admitted.” Crane, 476 U.S. at 690, 106 S.Ct. 2142. But it simultaneously observed that the “opportunity [to be heard] would be an empty one if the State were permitted to exclude competent, reliable evidence ... when such evidence is central to the defendant’s claim of innocence.” Id. The applicable constitutional standard is this: to establish that her right to compulsory process was violated by the exclusion of Diante’s testimony, Harris must show that (1) the testimony would have been “both material and favorable” to her defense, United States v. Valenzuela-Bernal, 458 U.S. 858, 867, 102 S.Ct. 3440, 73 L.Ed.2d 1193 (1982), and (2) that the exclusion was “arbitrary” or “disproportionate” to the evidentiary purpose advanced by the exclusion, Scheffer, 523 U.S. at 308, 118 S.Ct. 1261, quoting Rock, 483 U.S. at 56, 107 S.Ct. 2704. We conclude that Harris has made each showing. 1. Material and Favorable to the Defense In Valenzuelor-Bemal, the Supreme Court imported the materiality requirement of the Brady v. Maryland line of eases into the Compulsory Process Clause analysis. Under this standard, the exclusion of a witness is material “only if there is a reasonable likelihood that the testimony could have affected the judgment of the trier of fact.” Valenzuelcir-Bemal, 458 U.S. at 874, 102 S.Ct. 3440 (government’s deportation of defense witness did not violate Sixth Amendment because defendant did not show a reasonable probability that he would not have been convicted if the witness had testified). This materiality standard is also identical to the one used to determine whether ineffective assistance of counsel is “prejudicial” under Strickland. See 466 U.S. at 694, 104 S.Ct. 2052. (This equivalence between the two standards is helpful when we address Harris’s Strickland claim in Part IV, below.) Let’s first consider what Diante’s testimony would have been. It is undisputed that Diante was in the room when Jaquari died and that his account was entirely exculpatory to Harris. He would have testified that he saw Jaquari wrap the elastic band around his own neck, that his mother was not in the room when this happened, that Jaquari vomited in his “sleep,” and that he saw a bubble form on Jaquari’s mouth: This was all consistent with the physical evidence. Indeed, the medical examiner had initially concluded that the cause of death was self-asphyxiation. It was also consistent with Sta-Von Dancy’s testimony that Jaquari had wrapped the elastic band around his own neck on previous occasions and that a mucus bubble had formed when Dancy found Jaquari lying unconscious. No other witness testified to what actually happened in the moments before Jaquari died. As the trial court itself acknowledged, Diante’s testimony was “critical” to the defense. See S.A. 90-91. The testimony was new, favorable, and not cumulative. Diante’s testimony was also material. It is reasonably likely it would have significantly altered the balance of evidence to tip the scales in Harris’s favor. The analogy to Brady helps show why. Imagine for a moment that the prosecutor in Harris’s case had withheld from the defense the fact that Diante had told police investigators that he saw Jaquari strangle himself with the sheet’s elastic band. And imagine the prosecution’s evidence is the same as it was at trial: no other eyewitness contradicts Diante and says that Harris did it, and no physical evidence implicates Harris in Jaquari’s death. “If, for example, one of only two eyewitnesses to a crime had told the prosecutor that the defendant was definitely not its perpetrator and if this statement was not disclosed to the defense, no court would hesitate to reverse a conviction resting on the testimony of the other eyewitness.” United States v. Agurs, 427 U.S. 97, 113 n. 21, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976), quoting Victor Bass, Comment, Brady v. Maryland and The Prosecutor’s Duty to Disclose, 40 U. Chi. L.Rev. 112, 125 (1972). A fortiori, if the prosecution failed to disclose the existence of the case’s only eyewitness, whose testimony is unique, exculpatory, and uncontradicted, the suppression would clearly be material. In such a case, the Brady violation would be obvious. Cf. Smith v. Cain, — U.S. -, 132 S.Ct. 627, 630-31, 181 L.Ed.2d 571 (2012) (finding Brady violation in prosecution’s failure to disclose police notes that impeached only eyewitness). Smith shows that impeachment of the inculpatory testimony of the only eyewitness is material to an accused’s defense. It follows that an undisclosed exculpatory statement of the only eyewitness is certainly material as well. Cf. Kyles v. Whitley, 514 U.S. 419, 429, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (holding that State’s suppression of evidence that would have enabled impeachment of the government’s best witness violated Brady where the “heart of the State’s case was eyewitness testimony”). As the Supreme Court has made clear, “the materiality inquiry is not just a matter of determining whether, after discounting the inculpatory evidence in light of the undisclosed evidence, the remaining evidence is sufficient to support the jury’s conclusions.” Strickler v. Greene, 527 U.S. 263, 290, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999), citing Kyles, 514 U.S. at 434-35, 115 S.Ct. 1555. Rather, the question is whether the “favorable evidence ... ‘could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict.’ ” Cone, 556 U.S. at 470, 129 S.Ct. 1769, quoting Kyles, 514 U.S. at 435, 115 S.Ct. 1555. Had the prosecution in this case withheld Diante’s statements to authorities that Jaquari had asphyxiated himself, it would require reversal of Harris’s conviction under Brady. Diante’s testimony is also material under the Compulsory Process Clause, for the same standard applies. The trial court’s disqualification of Diante deprived Harris of direct evidence from the sole eyewitness. This evidence was central to her theory of the case — that Jaquari’s death was a tragic accident. No other witness replicated Diante’s testimony. And no other witness contradicted Diante’s account at trial; only the medical examiner supported the prosecution’s theory that the Jaquari’s death was even a homicide, and Dr. Denton admitted that this was a revised opinion. Diante’s testimony was at least as valuable to Harris’s defense as were the undisclosed statements from the State’s eyewitness in Smith v. Cain, and it was just as likely to cast “the whole case in such a different light as to undermine confidence in the verdict.” Cone, 556 U.S. at 470, 129 S.Ct. 1769, quoting Kyles, 514 U.S. at 435,115 S.Ct. 1555. In its harmless error analysis of the state evidentiary issue, the Illinois Appellate Court wrote that “the proposed testimony of Diante was [not] likely to have [had] any significant impact upon the strength of the State’s case” because of the “inherent weakness in the Diante proffer.” Harris, 328 Ill.Dec. 567, 904 N.E.2d at 1094. The only value to Diante’s testimony, the court found, was the “observation of Jaquari wrapping an elastic band around his neck.” Id. But the court saw this testimony as not particularly important because “jurors had learned from other witnesses that Jaquari had done such things before.” Id. And the force of Di-ante’s account would have been “negated or otherwise diminished by Diante’s admission to Ms. Wilson,” who interviewed him two days after the death, “that ‘he was asleep when his brother got hurt.’ ” Id., 328 Ill.Dec. 567, 904 N.E.2d at 1095. (Di-ante also told Ale Levy, who interviewed him the day before Wilson, that he was “asleep when Jaquari died.”) We respectfully find this analysis to lack merit. Diante’s testimony that he saw his brother wrapping the very instrument of death around his neck just before he died is far more relevant than Dancy’s testimony that Jaquari had wrapped the band around his neck on some previous occasions. Evidence is cumulative when it “goes to prove what has already been established by other evidence.” Mosley v. Atchison, 689 F.3d 838, 848 (7th Cir.2012), quoting Smith v. Sec’y of New Mexico Dep’t of Corrections, 50 F.3d 801, 829 (10th Cir.1995); see also Arizona v. Fulminante, 499 U.S. 279, 299, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991). None of the other defense witnesses came close to Diante in terms of their exculpatory value. Diante’s testimony would not have been cumulative. Nor does Diante’s “admission” to Wilson that he was asleep when Jaquari died significantly reduce the probative force of his testimony. At most, it suggests that Di-ante, like many children, did not fully comprehend the concept of death and that, heartbreakingly, he may well have watched his brother die without realizing it. See Mark W. Speece & Sandor B. Brent, Children’s Understandings of Death: A Review of Three Components of a Death Concept, 55 Child. Dev. 1671, 1679 (1984) (studies show that children acquire some understanding of conceptual components of death between ages five and seven, with “wide range of ages of acquisition” observed). Diante believed Jaquari fell “asleep” with the mucus bubble, and only later was he informed of Jaquari’s death. Given Diante’s age, a reasonable jury would understand perfectly well what was going on here. At worst, Diante’s “admission” to being asleep created a superficial tension with his earlier (and unambiguous) report that he saw Jaquari wrap the elastic around his own neck and that his mother was not present. At trial, the prosecution could certainly have explored that tension and the jury may have considered it in evaluating his testimony. But the idea that this would have “negated” the rest of his testimony is groundless. By excluding Diante’s testimony altogether, the trial court denied Harris the opportunity to present the strongest evidence of her innocence and impeded the jury in its search for truth. The appellate court minimized the significance of this exclusion by pointing to Di-ante’s ambiguous “admission” and seizing on the most favorable interpretation to the prosecution. That is not how harmless error review works, and it is not how our materiality analysis proceeds under the Compulsory Process Clause. That inquiry asks whether the exclusion of the evidence had a reasonable probability of affecting the outcome of trial, and the disqualification of Diante did. The State argues also that Diante’s testimony, even if credited, would not have made a difference because the evidence against Harris was “overwhelming.” Exculpatory evidence may be inconsequential to the outcome of the trial “if the State’s other evidence is strong enough to sustain confidence in the verdict.” Smith, 132 S.Ct. at 630, citing Agurs, 427 U.S. at 112-13, 96 S.Ct. 2392. But that is certainly not this case. The prosecution presented no physical evidence that linked Harris to Jaquari’s death. The medical examiner initially concluded that Jaquari’s death was a “tragic accident.” The testimony of Dancy, the only person present at the apartment aside from the accused and the two children, supported Harris’s account. The prosecution’s case rested entirely on Harris’s videotaped confession. To be sure, a “voluntary confession” is “highly probati