
590 F.3d 533 (2010)
Scott J. REVER, Petitioner-Appellant,
v.
Gerardo ACEVEDO, Warden, Respondent-Appellee.
No. 09-1156.
United States Court of Appeals, Seventh Circuit.
Argued August 4, 2009.
Decided January 4, 2010.
Jonathan A. Backman (argued), Bloomington, IL, for Petitioner-Appellant.
Erin O'Connell (argued), Assistant Attorney General, Office of the Attorney General, Chicago, IL, for Respondent-Appellee.
Before FLAUM, KANNE, and WOOD, Circuit Judges.
PER CURIAM.
Scott Rever, an Illinois inmate, appeals from the denial of his petition for a writ of habeas corpus. After he was charged with 15 counts related to the kidnap and rape of his ex-girlfriend, Rever was twice found unfit for trialthe second finding came after a suicide attemptand remanded to a state-run facility for treatment. When officials at the facility issued a report finding him competent to stand trial, his lawyer *534 stipulated to his competence despite the lawyer's professed failure to understand the report. The court accepted the stipulation and Rever went to trial without a fitness hearing. He was convicted on 11 of the 15 counts and sentenced to 33 years. In an unsuccessful appeal, Rever's counsel did not mention the lack of a fitness hearing. In post-conviction proceedings, the trial court acknowledged that it should have held a full hearing on Rever's fitness despite counsel's stipulation, but found that counsel's failure to pursue the issue was not prejudicial. After the appellate court affirmed and the state supreme court denied his petition for leave to appeal, Rever filed his federal petition, which the district court denied. We affirm because Rever failed to rebut the state trial court's factual finding that he presented insufficient evidence to show that appellate counsel's conduct prejudiced him.

I. BACKGROUND
On April 29, 1999, Rever's ex-girlfriend and her current boyfriend heard a window break in her apartment. They went outside and saw Rever. After a struggle, Rever grabbed his ex-girlfriend and dragged her, at knifepoint, to his car. He drove to a rural area where he beat his ex-girlfriend, tore off her clothing, and raped her. Rever was charged with fifteen counts, including two counts of aggravated kidnapping, seven counts of aggravated criminal sexual assault, and three counts of aggravated battery.
Before Rever could be tried, Dr. Robert Chapman, a forensic psychiatrist, examined him and concluded that he suffered severe and possibly suicidal depression that made him incompetent to stand trial. Dr. Chapman also concluded that with psychiatric treatment and antidepressant medication, Rever could become competent within one year. Based on Dr. Chapman's report, the court found Rever unfit to stand trial and remanded him to the McLean County Department of Mental Health for "treatment and restoration to fitness." Three months later, the court held a follow-up hearing on Rever's fitness. The Department of Mental Health had filed a report stating that Rever was fit. After counsel stipulated to the report and waived a further hearing, the court found Rever fit to stand trial. The court's finding that Rever was fit to stand trial was called into question about one month later when Rever attempted suicide. Dr. Chapman examined Rever again and reached a conclusion similar to his earlier one. According to Dr. Chapman, Rever continued to suffer profound and prolonged depression with "substantial hopelessness and suicidal risk," which made him unable to assist with his defense. Dr. Chapman added, again, that a successful course of antidepressants could make Rever fit to stand trial. Based on Dr. Chapman's report, the trial court again found Rever unfit to stand trial and again remanded him to the McLean County Department of Mental Health for treatment.
Three months after the court found Rever unfit for the second time, a doctor and an administrator at the Department of Mental Health prepared a progress report stating that Rever had been restored to fitness. The trial court held another hearing at which Rever's counsel stipulated to the progress report even though it contained what he believed was an inconsistency: it concluded that Rever was both fit for trial and still in need of inpatient care. Counsel told the court, "I'm going to stipulate to it because it seems to be contradictory in terms but not being a psychiatrist, I don't presume to interpret." When the judge followed up on the seeming inconsistency, asking counsel what the report meant when it said Rever was in need of *535 inpatient care, counsel answered, "I have no clue." Counsel repeated his statement that he had "no clue" about what he took to be an inconsistency in the report, but he did not waver in his desire to stipulate to the report. Based on counsel's stipulation to the report, the judge found Rever fit to stand trial.
At the hearing, counsel also told the judge that since the report had been prepared, Rever's psychiatrist at the Department of Mental Health had raised Rever's daily dosage of Effexor, a common antidepressant, from 75 mg to 225 mg. Counsel asked for an order that would require the jail to comply with the change. Counsel also told the court he was going to have Dr. Chapman examine Rever again to determine the effect of the increased dosage, but that examination never took place.
After the jury found Rever guilty on 11 of the 15 counts, Rever saw Dr. Chapman again in preparation for sentencing. In his report, Dr. Chapman did not opine on Rever's fitness to stand trial or to be sentenced, but he did diagnose Rever as suffering from bipolar disorder. Dr. Chapman testified as a mitigation witness at sentencing, but did not opine on Rever's fitness. The court sentenced Rever to 33 years in prison.
In his direct appeal, Rever did not discuss his fitness to stand trial. The appellate court affirmed and also did not mention the issue. After the Illinois Supreme Court denied his petition for leave to appeal, Rever sought post-conviction relief in the trial court. In his petition, Rever argued that his trial counsel was ineffective for allowing him to be tried without a full fitness hearing and that appellate counsel was ineffective for failing to raise the issue on appeal. The trial court found that Rever's petition stated the gist of a constitutional claim, so the court appointed counsel and held a hearing. At the hearing, Dr. Chapman testified that the seemingly contradictory findings in the progress report were not necessarily inconsistent: a defendant could be both fit to stand trial and in need of inpatient treatment. Dr. Chapman also explained that he had not formed an opinion on Rever's fitness to stand trial at the time of the agency report and that he was not prepared to do so retrospectively. On the other hand, though, Dr. Chapman explained that he or another medical professional could formulate such an opinion retrospectively.
After hearing argument on the petition, the judge, who had also overseen the criminal trial, acknowledged that he had "made an error by not having a restoration of fitness hearing." Nevertheless, he denied Rever's petition, stating that "there is no evidence" that Rever was unfit at the time of trial. Moreover, the judge noted that Rever's conduct during trial demonstrated his fitness. Accordingly, the trial court found that neither trial counsel's failure to demand a hearing nor appellate counsel's failure to raise the issue constituted ineffective assistance.
Rever appealed, arguing only that his appellate counsel was ineffective for failing to raise competence. The Illinois Appellate Court affirmed the trial court's ruling but on slightly different grounds. First, the court held that the trial court did not err by accepting counsel's stipulation to Rever's fitness, so appellate counsel's failure to raise the issue was not objectively unreasonable. Under Illinois law, a fitness finding cannot be based on a stipulation to the existence of a psychiatric conclusion, the court explained, but the stipulation in this case was to a report that the trial court had read and discussed with counsel. In addition, the court had observed the defendant before accepting the stipulation. On the second prong of the test for ineffective assistance, the appellate court held that Rever could not show prejudice because the trial court had properly found *536 both before trial and during the post-conviction proceedings that he was fit for trial. The Illinois Supreme Court denied Rever's petition for leave to appeal.
Rever then filed a petition for a writ of habeas corpus in federal court. He argued again that trial counsel was ineffective for failing to seek a fitness hearing before trial and that appellate counsel was ineffective for failing to raise the issue. The district court ordered the state to respond, held a hearing by telephone, and denied the petition because Rever had failed to present substantial facts that would show he was unfit to stand trial. The court acknowledged that trial counsel may have erred, but ruled that Rever had not shown that any error was prejudicial because he had failed to present evidence showing that he was unfit to stand trial. The court went on to deny Rever's alternative request for an evidentiary hearing on his fitness because Rever did not satisfy the requirements of 28 U.S.C. § 2254(I). But the district court did grant Rever a certificate of appealability on two issues:
(1) Whether petitioner sufficiently demonstrated a real and substantial doubt as to his fitness to stand trial, which would then shift the burden to the State to demonstrate that he was in fact fit at the time of trial; and
(2) Whether, if petitioner did not sufficiently demonstrate such doubt, this Court erred in denying him an evidentiary hearing at which he might establish this doubt, in light of the Section 2254 standard, whereby the effectiveness or incompetence of counsel during Federal or State collateral post conviction proceedings are not grounds for relief.
(Id. at 19.)

II. ANALYSIS
On appeal, both parties direct their efforts to the issues on which the district court granted the certificate of appealability. That is unfortunate because the district court identified the wrong issues. Rever argued in his petition that his trial counsel was ineffective for going to trial without a fitness hearing and that appellate counsel was also ineffective for failing to raise the issue. (The first argument was not presented to the Illinois Appellate Court and is, therefore, procedurally defaulted. See Gonzales v. Mize, 565 F.3d 373, 380 (7th Cir.2009).) Rather than examining the state courts' analysis of Rever's claims of ineffective assistance, the district court applied pre-AEDPA law to assess Rever's underlying fitness claim. Specifically, the district court applied Lewis v. Lane, 822 F.2d 703 (7th Cir.1987), which adopted a burden shifting approach to fitness claims presented in federal habeas: once the petitioner presents substantial facts supporting his allegation of incompetency, the burden shifts to the state to show that the petitioner was in fact competent to stand trial. Id. at 706-07. But under AEDPA, federal courts do not independently analyze the petitioner's claims; federal courts are limited to reviewing the relevant state court ruling on the claims. See Dunlap v. Hepp, 436 F.3d 739, 744 (7th Cir.2006) (citing Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). The independent review applied in Lewis did not survive AEDPA. See Sturgeon v. Chandler, 552 F.3d 604, 612 (7th Cir.2009) (reviewing state court determination of competency); Woods v. McBride, 430 F.3d 813, 820 (7th Cir.2005) (same). Thus, the district court should have limited its review to the rulings of the Illinois courts that considered Rever's arguments.
Although Rever casts his arguments in the wrong direction, they are easily recast as challenging the state court proceedings. *537 At bottom, Rever's argument is that the state courts violated his constitutional right to a reasonable opportunity to demonstrate that he was unfit to be tried. See Medina v. California, 505 U.S. 437, 451, 112 S.Ct. 2572, 120 L.Ed.2d 353 (1992); Drope v. Missouri, 420 U.S. 162, 180, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975); Woods, 430 F.3d at 819. Illinois implements that right by statute: once a defendant presents a "bona fide doubt" about his fitness, the burden shifts to the state to prove fitness by a preponderance of evidence. 725 ILCS 5/104-11; see also Sturgeon, 552 F.3d at 610 ("[S]ection 104-11 protects a constitutional right."). That standard also applies to post-conviction claims, see People v. Shum, 207 Ill.2d 47, 278 Ill.Dec. 14, 797 N.E.2d 609, 616 (2003), and the trial court applied it when the court denied Rever's request for post-conviction relief based on its finding that "[t]here is no evidence that [Rever] was unfit when trial commenced." In other words, the trial court found that, in the retrospective hearing, Rever failed to submit evidence showing a bona fide doubt as to his fitness, so a full retrospective hearing on his fitness before trial was not necessary.
The Illinois Appellate Court seems to have considered the trial court's finding to be an explicit fitness determination, and Rever attacks the appellate court's ruling on that basis. Despite our doubts about that portion of the appellate court's ruling, we need not delve into it because, while our review adjudication in state court is limited to the last decision to address the arguments on the merits, see Smiley v. Thurmer, 542 F.3d 574, 580 (7th Cir.2008), our deference to factual findings in state court, see 28 U.S.C. § 2254(e)(1), is not so limited. Section 2254(e)(1)'s text makes that clear: "a determination of a factual issue made by a State court shall be presumed to be correct." Id. (emphasis added); see Hannon v. Sec'y, Dep't of Corr., 562 F.3d 1146, 1150 (11th Cir.2009); see also Sumner v. Mata, 449 U.S. 539, 547, 101 S.Ct. 764, 66 L.Ed.2d 722 (1981) (pre-AEDPA). And that deference to state courts' factual findings applies even when we refuse to defer to the state courts' legal adjudication. See Brown v. Smith, 551 F.3d 424, 431 (6th Cir.2008); Hodges v. Attorney Gen., State of Fla., 506 F.3d 1337, 1348 (11th Cir.2007); Jacobs v. Horn, 395 F.3d 92, 100 (3d Cir.2005). Thus, even if Rever can overcome our AEDPA deference to the appellate court's adjudication of his claim, we still presume to be correct the trial court's finding that he did not present sufficient evidence at the retrospective hearing to raise a bona fide doubt as to his competence and, therefore, failed to show that he was prejudiced by appellate counsel's conduct. See People v. Harris, 206 Ill.2d 293, 276 Ill.Dec. 286, 794 N.E.2d 181, 189-90 (2002); People v. Pitsonbarger, 205 Ill.2d 444, 275 Ill.Dec. 838, 793 N.E.2d 609, 628-30 (2002).
Rever attacks that finding on two fronts, but both attacks fail. First, he points to the report by the Department of Mental Healththe only evidence that he was fit to stand trial. According to Rever, the report contains "innumerable problems," but he enumerates only two. The first is the seeming inconsistency between the report's conclusion that Rever was fit for trial but also in need of inpatient care. But Rever's own expert explained in the post-conviction proceedings that these two findings were not necessarily inconsistent. The second purported problem is the report's explanation that Rever did not "fully understand that facing his charges and resolving his legal problems is the best way to diminish his depressive feelings," but Rever does not explain how that statement might be inconsistent with a finding of competency. In fact, the statement is not about fitness to stand trial; it is about *538 treating Rever's depression, and not every mental illness demonstrates incompetence to stand trial. See Eddmonds v. Peters, 93 F.3d 1307, 1314 (7th Cir.1996).
Rever's second argument against the state court's finding that he failed to present enough evidence to call his competency into question relies on the sharp increase in his medication shortly before trial. In Burt v. Uchtman, 422 F.3d 557 (7th Cir. 2005), this court held that the trial court should have conducted a competency hearing based in part on the petitioner's "heavy and ever-changing doses of psychotropic medication." Id. at 565-66. But in Burt, there was other evidence suggesting incompetencemost importantly, on the fourth day of trial, the petitioner suddenly decided to plead guilty against counsel's advice. By contrast, Rever's conduct during trial did nothing to call his competence into question. The increase in the dosage of Rever's medication, on its own, is not sufficient evidence to rebut the state court's finding.
Rever had the opportunity during the state post-conviction proceedings to present medical evidence challenging the report that found him fit. And had he presented sufficient evidence, he would have shifted the burden to the state to prove his fitness. Rever could have presented evidence on the dosage increase or anything else, but he did not do so, and his attempt to submit that evidence in federal habeas review comes too late. Rever's argument that the district court erred in denying him a hearing to present more evidence under 28 U.S.C. § 2254(e)(2) is meritless because he concedes that he cannot satisfy any of that provision's exceptions. Rever has failed to show the clear and convincing evidence necessary to rebut the state trial court's finding on the evidence he presented in the retrospective hearing. 28 U.S.C. § 2254(e)(1). Accordingly, we must defer to that finding and hold that Rever did not present sufficient evidence to show prejudice from appellate counsel's failure to raise the issue of competence.

III. CONCLUSION
Accordingly, we AFFIRM the district court's denial of Rever's petition.
