KANNE, Circuit Judge.

Petitioner Percell Dansberry pled guilty to murder and related charges in Illinois state court. During Dansberry's plea colloquy, the trial court, in violation of his constitutional rights, erroneously admonished him about the mandatory minimum sentence he faced. Dansberry petitioned for a writ of habeas corpus under 28 U.S.C. § 2254, arguing that the state court's error requires automatic reversal of his conviction and a chance to re-plead. The district court denied Dansberry's petition because it found that the error was harmless. We affirm.

I. BACKGROUND

The Supreme Court held in Boykin v. Alabama, 395 U.S. 238, 89 S.Ct. 1709, 23 L.Ed.2d 274 (1969), that the Constitution prohibits a court from accepting a criminal's defendant's guilty plea "without an affirmative showing that it was intelligent and voluntary." Id. at 242, 89 S.Ct. 1709. The Court demanded "the utmost solicitude" to ensure that the defendant "has a full understanding of what the plea connotes and of its consequences." Id. at 243-44, 89 S.Ct. 1709. A few years later, the Court reiterated in Brady v. United States, 397 U.S. 742, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970), that the defendant must be "fully aware of the direct consequences" of his plea, id. at 755, 90 S.Ct. 1463 (citation omitted), including the "permissible range of sentences," Boykin, 395 U.S. at 244 n. 7, 89 S.Ct. 1709 (citation omitted).

The federal courts and many states responded to Boykin by adopting or modifying procedural rules designed to ensure compliance with due process when accepting guilty pleas. The federal system adopted a more robust Federal Rule of Criminal Procedure 11, and Illinois adopted Supreme Court Rule 402. See United States v. Wagner, 996 F.2d 906, 913 (7th Cir.1993) (recognizing that the new Rule 11 "codified the requirements of Boykin"); People v. Burt, 168 Ill.2d 49, 212 Ill.Dec. 893, 658 N.E.2d 375, 382 (1995) ("Rule 402 was adopted to insure compliance with these due process requirements.").

In this case, the state trial court admonished Dansberry, as required by due process and Illinois Supreme Court Rule 402, before accepting his guilty plea. But the court erred when explaining what possible sentences he faced.

A. State Court Proceedings

Dansberry shot and killed 18-year-old Antonio Bass during an attempted armed robbery in Chicago in 1997. An eyewitness saw the crime, and when questioned by police, Dansberry admitted his culpability. Dansberry was charged in state court with first-degree murder and attempted armed robbery. He initially pled not guilty. But on the day his criminal trial was scheduled to begin, Dansberry changed his mind and entered a "blind" plea of guilty (meaning he did not know what his sentence would be).

The trial court held a change-of-plea hearing. The court advised Dansberry on the record about the rights he was giving up, the charges against him, and the range of possible sentences. The court explained that the murder conviction carried a prison term of 20 to 60 years, life, or the death penalty. On the attempted armed robbery charge, he faced another 6 to 30 years of incarceration. The court added that it was "possible" the two sentences could run consecutively. By the court's calculations, then, Dansberry faced a minimum of 20 years in prison up to 90 years, life imprisonment, or death. Dansberry said he understood.

In fact, however, the court's calculations were incorrect. On the low end, because 730 ILCS 5/5-8-4 made consecutive sentences mandatory (not merely "possible," as the court mistakenly said), Dansberry faced a minimum prison term of 26 years, not 20. On the upper end, Dansberry was eligible for an extended prison term of up to 100 years for first-degree murder, see 730 ILCS 5/5-8-2; 730 ILCS 5/5-4.5-20, bringing his maximum term to 130 years, not 90. The court was correct, however, about the possibility of life imprisonment or the death penalty.

After accepting Dansberry's plea, the court held a sentencing hearing. It found him eligible for the death penalty but sentenced him instead to consecutive prison terms of 65 years for murder and 15 years for the robbery charge, for a total of 80 years.

Dansberry later moved to withdraw his guilty plea on the ground that (1) his plea was involuntary and unknowing, and (2) trial counsel was constitutionally ineffective. The trial court held a hearing on the motion. The evidence showed that leading up to the trial, the State had pressed for the death penalty. Trial counsel told Dansberry that he could be sentenced to more than 60 years of incarceration, life, or death. Dansberry's main concern, according to counsel, was to avoid execution. That is what drove his decision to plead guilty. Dansberry says his attorney told him to expect a sentence of around 40 years in exchange for his plea, though his attorney denied making any such prediction. Dansberry later told a friend that he "took the 40."

The trial court denied Dansberry's motion to withdraw his plea. The Illinois Appellate Court affirmed. People v. Dansberry, No. 97 CR 17153, 403 Ill.App.3d 1101, 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. (Ill.App.Ct. Oct. 18, 2010) ("Dansberry I"). Citing Boykin, the appellate court noted that "[i]n order to satisfy due process, a guilty plea must be affirmatively shown to have been made voluntarily and intelligently." Id. 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 13. The court noted further that Illinois "Supreme Court Rule 402 was adopted to ensure compliance with these due process requirements" by, inter alia, requiring the trial court to admonish a defendant about the "minimum and maximum sentence prescribed by law." Id. 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 13-14 (quoting Ill. Sup.Ct. R. 402(a)(2)).

The state appellate court found that the trial court "substantially complied" with Rule 402 and due process because it told Dansberry that he could face a sentence longer than 60 years and because an ordinary person in his position would have understood that he "could be subjected to a minimum sentence of 26 years." Id. 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 15-16. Moreover, the court found no showing by Dansberry "as to how he was denied real justice or suffered prejudice." Id. 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 16. One of the justices dissented, arguing that prejudice is inherent when a defendant "has not been informed of the full consequences of his guilty plea." Id. 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 24 (Hall, P.J., dissenting). The Illinois Supreme Court denied Dansberry's petition for leave to appeal. People v. Dansberry, 239 Ill.2d 562, 348 Ill.Dec. 193, 943 N.E.2d 1103 (Ill.2011).

B. Federal Habeas Proceedings

After losing his state-court appeal, Dansberry filed a habeas corpus petition under 28 U.S.C. § 2254 in the Northern District of Illinois challenging both his trial counsel's performance and the validity of his guilty plea. The district court rejected both arguments, but only the latter one is before us on appeal.

The district court disagreed with the Illinois Appellate Court, holding that "[t]o the extent [it] found no due process violation in Dansberry's case," that was "an unreasonable application of clearly established Supreme Court precedent." Dansberry v. Pfister, No. 11 C 8719, 2013 WL 5966974, at *6, 2013 U.S. Dist. LEXIS 159811, at *22 (N.D.Ill. Nov. 8, 2013) ("Dansberry II"). The district court held that the state trial court violated Boykin and Brady. Id. Specifically, the trial court incorrectly led Dansberry to believe that his minimum prison sentence was 20 years when in fact, considering that consecutive sentences were mandatory, he faced at least 26 years. There was no evidence that Dansberry was otherwise aware of the correct figure. Following the Third Circuit in Jamison v. Klem, 544 F.3d 266 (3d Cir.2008), the district court held that because Dansberry was "unaware of a mandatory minimum sentence," he "cannot be said to have been fully aware of the direct consequences of his ... guilty plea." Dansberry II, at *6, 2013 U.S. Dist. LEXIS 159811, at *21 (internal quotation marks and citation omitted).

The district court found no constitutional error, however, in the trial court's admonition concerning the upper end of Dansberry's sentencing range. Although the trial court mistakenly understated the maximum statutory prison term (which was 130 years rather than 90), it did tell Dansberry that he faced a possible life sentence or the death penalty. Following our decision in Steward v. Gilmore, 80 F.3d 1205, 1214 (7th Cir.1996), the district court held that this was enough to apprise the defendant of his maximum possible sentence and to comport with due process. Dansberry II, at *5-6, 2013 U.S. Dist. LEXIS 159811, at *16-18.

Having found that the trial court erred in admonishing Dansberry about his mandatory minimum sentence, the district court nevertheless denied his petition for habeas relief. That is because the district court concluded: (1) that the Boykin error was subject to review for harmlessness; and (2) that the error here was harmless. Id. at *4-6, 2013 U.S. Dist. LEXIS 159811, at *13-18. Dansberry challenges both of those holdings on appeal.1

II. ANALYSIS

We review the denial of a habeas petition de novo. Smith v. McKee, 598 F.3d 374, 381 (7th Cir.2010). A state prisoner may seek habeas relief on the ground that his detention violates the federal Constitution or laws. 28 U.S.C. § 2254(a). But under the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), a federal court may not grant habeas relief on any claim that has already been adjudicated on the merits in state court unless the adjudication "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 State court proceeding." 28 U.S.C. § 2254(d). Under AEDPA, habeas relief from a state-court judgment is "not easy to come by." Kamlager v. Pollard, 715 F.3d 1010, 1015 (7th Cir.2013) (internal quotation marks and citation omitted).

The decision under review is "the decision of the last state court to adjudicate the merits of the petitioner's claim." Id. "Clearly established federal law" for AEDPA purposes "refers to the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision." Carey v. Musladin, 549 U.S. 70, 74, 127 S.Ct. 649, 166 L.Ed.2d 482 (2013) (internal quotation marks and citation omitted). But later Supreme Court decisions and decisions by lower courts may also be helpful in determining the content or application of clearly established federal law. See, e.g., id. at 76-77, 127 S.Ct. 649 (treating divergence among lower courts as evidence that there was no clearly established federal law).

A. Availability of Harmless-Error Review

Dansberry contends that the trial court's Boykin error requires automatic reversal of his conviction and a chance to re-plead. The Illinois Appellate Court rejected that argument and instead undertook a harmless-error analysis. Dansberry I 373 Ill.Dec. 147, 993 N.E.2d 147, slip op. at 14-18. Although the court did not explain its reasons, we still afford AEDPA deference to its conclusion. See Harrington v. Richter, 562 U.S. 86, 99, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011) (presuming state court adjudicated claim on the merits in the absence of any indication to the contrary). We therefore need only determine whether the state appellate court's decision was contrary to or an unreasonable application of clearly established Supreme Court precedent. See 28 U.S.C. § 2254(d)(1). The district court below held that it was not. Dansberry II, at *6-7, 2013 U.S. Dist. LEXIS 159811, at *22-25. We agree.

In the context of criminal trials, the Supreme Court "has recognized that most constitutional errors can be harmless." Arizona v. Fulminante, 499 U.S. 279, 306, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991). "If the defendant had counsel and was tried by an impartial adjudicator, there is a strong presumption that any other constitutional errors ... are subject to harmless-error analysis." Neder v. United States, 527 U.S. 1, 8, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (internal punctuation and citation omitted). The Court has proven this maxim by applying harmless-error analysis to a wide variety of constitutional transgressions. Fulminante, 499 U.S. at 306-07, 111 S.Ct. 1246 (collecting cases). "[O]nly in a very limited class of cases" has the Court found an error to be "structural," requiring automatic reversal. Neder, 527 U.S. at 8, 119 S.Ct. 1827 (internal quotation marks and citation omitted).

An error is structural when it "def[ies] analysis by `harmless-error' standards" because it "affect[s] the framework within which the trial proceeds" and is not "simply an error in the trial process itself." Fulminante, 499 U.S. at 310, 111 S.Ct. 1246. Such errors include the denial of a defendant's right to counsel, to self-representation, to a public trial, or to a trial by jury. United States v. Gonzalez-Lopez, 548 U.S. 140, 149, 126 S.Ct. 2557, 165 L.Ed.2d 409 (2006) (citations omitted). Other errors, such as the erroneous deprivation of a defendant's counsel of choice, are structural because their effects are "necessarily unquantifiable and indeterminate." Id. at 150, 126 S.Ct. 2557 (internal quotation marks and citation omitted).

We are aware of no Supreme Court decision directly addressing whether a Boykin error is structural. But at least one of our sister circuits has held that it is not. See United States v. Johns, 625 F.2d 1175, 1176 (5th Cir.1980) (holding that "[e]ven if the district court erred under Boykin ... it would not be reversible error" because the record established that it was "harmless beyond a reasonable doubt"). And this court, in Stewart v. Peters, rejected a due process claim where the court erroneously admonished the defendant about his mandatory minimum sentence but the error was immaterial — i.e., it would not have changed the defendant's plea. 958 F.2d 1379, 1385 (7th Cir. 1992).

Similarly, we think an erroneous admonishment of the kind we have here — an incorrect statement of a defendant's mandatory minimum sentence — is non-structural. It does not affect the entire proceedings in the way that, e.g., an out-right denial of counsel would. Cf. Gonzalez-Lopez, 548 U.S. at 149, 126 S.Ct. 2557 (giving examples of structural errors). And its effects are likely to be identifiable and measurable. Cf. id. at 150, 126 S.Ct. 2557 (finding structural error where the effects are "necessarily un-quantifiable and indeterminate"). In short, an erroneous admonishment about a mandatory minimum sentence does not defy analysis for harmless error.

In an analogous context, Federal Rule of Criminal Procedure 11 requires the court, before entering a guilty plea, to admonish the defendant about the minimum and maximum penalties he faces (among other things). Fed.R.Crim.P. 11(b)(1)(H)-(I). If the court fails to do that, then Rule 11(h) calls for harmless-error analysis. Fed. R.Crim.P. 11(h) (stating that a "variance from the requirements of this rule is harmless error if it does not affect substantial rights"). Courts regularly perform that analysis. See, e.g., United States v. Padilla, 23 F.3d 1220, 1221-22 (7th Cir.1994) (reviewing failure to inform defendant about mandatory minimum sentences for harmless error). This shows that such errors are susceptible to, and do not defy, harmless-error review.

That is not to say that every Boykin error will always be reviewed for harmless error. In United States v. Dominguez Benitez, a case involving Rule 11 error, the Supreme Court suggested in a footnote that some due process violations during a plea colloquy might require automatic reversal of a conviction. 542 U.S. 74, 84 n. 10, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004). For example, where the record of the plea hearing "contains no evidence that a defendant knew of the rights he was putatively waiving," as in Boykin itself, then "the conviction must be reversed." Id. The Court continued: "We do not suggest that such a conviction could be saved even by overwhelming evidence that the defendant would have pleaded guilty regardless." Id.; cf. Brecht v. Abrahamson, 507 U.S. 619, 638 n. 9, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (recognizing that "in an unusual case, a deliberate and especially egregious error of the trial type" might require automatic reversal).2

This, however, is not such a case. Dansberry was aware of the rights he waived by pleading guilty. The error here concerned the precise penal consequences of his plea — a less fundamental error. Moreover, the footnote in Dominguez Benitez is dictum and therefore does not constitute "clearly established" federal law for purposes of AEDPA. Musladin, 549 U.S. at 74, 127 S.Ct. 649.

For these reasons, we uphold the Illinois Appellate Court's conclusion that the Boykin error during Dansberry's plea colloquy did not require automatic reversal of his conviction but was instead subject to harmless-error review.

B. Harmless-Error Analysis

All that remains is to determine whether the error here was harmless. The Illinois Appellate Court thought so, but it applied the wrong standard, requiring Dansberry to show that he was denied "real justice" or that he suffered "prejudice." Dansberry I, 348 Ill.Dec. 193, 943 N.E.2d 1103, slip op. at 14, 16. The correct standard on direct appeal of a constitutional claim is the Chapman standard: whether the error was "harmless beyond a reasonable doubt." Johnson v. Acevedo, 572 F.3d 398, 403 (2009) (citing Chapman v. California, 386 U.S. 18, 23, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967)). Because the state court applied a contrary standard, its conclusion merits no AEDPA deference. Id. at 404; see also Ruhl v. Hardy, 743 F.3d 1083, 1091 (7th Cir.2014). Instead, we make our own independent decision regarding harmless error, as if the state court had never addressed the issue. Acevedo, 572 F.3d at 404. On collateral review the Brecht standard applies: we ask whether the error "had substantial and injurious effect or influence" on the outcome of the proceeding. Id. at 403 (quoting Brecht, 507 U.S. at 623, 113 S.Ct. 1710).

We are confident that the error here had no such effect on Dansberry's decision to plead guilty, for largely the same reasons given by the district court. Dansberry II, at *8-9, 2013 U.S. Dist. LEXIS 159811, at *29-32. The state trial and appellate courts found no evidence that Dansberry would have changed his plea had he known that he faced a mandatory minimum sentence of 26 years rather than 20 years. And on habeas review, we presume that a state court's factual determinations are correct. 28 U.S.C. § 2254(e)(1).

What is more, the record shows that Dansberry's minimum sentence had little, if any, influence on his decision. He was much more concerned about his maximum sentence; he wanted to avoid being executed. He pled guilty largely because he expected he would receive about 40 years of incarceration instead. When he did plead, he did so "blindly," without any promise of a particular sentence, even though he had been informed that he could receive life imprisonment or even the death penalty. Ultimately, he was sentenced to 80 years in prison. It is highly unlikely, and there is no evidence in the record to suggest, that Dansberry's mistaken belief that his minimum sentence was 20 years rather than 26 years had any effect on his decision to plead guilty.

III. CONCLUSION

The district court's denial of Dansberry's petition for a writ of habeas corpus is AFFIRMED.