
580 F.3d 403 (2009)
John David RUELAS, Petitioner-Appellee,
v.
Hugh WOLFENBARGER, Respondent-Appellant.
No. 08-1571.
United States Court of Appeals, Sixth Circuit.
Argued: June 11, 2009.
Decided and Filed: September 8, 2009.
*405 ARGUED: Jerrold E. Schrotenboer, Jackson County Prosecutor's Office, Jackson, Michigan, for Appellant. Nathan S. Mammen, Kirkland & Ellis LLP, Washington, D.C., for Appellee. ON BRIEF: Jerrold E. Schrotenboer, Jackson County Prosecutor's Office, Jackson, Michigan, for Appellant. Nathan S. Mammen, Charles A. Fernández, Kirkland & Ellis LLP, Washington, D.C., for Appellee.
Before MARTIN and KETHLEDGE, Circuit Judges; WATSON, District Judge.[*]

OPINION
BOYCE F. MARTIN, JR., Circuit Judge.
John David Ruelas pleaded guilty to "open murder" for causing his mother's death. At his "degree hearing," where a judge was to find the proper level of criminal homicide for Ruelas based on his plea, he was found guilty of second-degree murder. Ruelas has now filed a petition for a writ of federal habeas corpus, contending *406 that his plea was not made knowingly or voluntarily and was thus unconstitutional. The district court agreed, and granted him a conditional writ of habeas corpus. Because we believe that even if his plea was involuntary any constitutional error was harmless, we REVERSE.

I.
In 2002, Ruelas, then thirty-eight years old, moved back into his mother's house after he and his wife divorced. Ruelas and his mother frequently argued, and in January of that year, he referred to his ex-wife as a "bitch." His mother scolded him, and he gave her "a couple of strikings." J.A. 217. As a result, his mother, seventy-six years old, died.
Ruelas was arrested and, in July 2002, pleaded guilty to "open murder" in exchange for the dismissal of a second felony offender charge. In Michigan, "open murder" pleas permit a judge to determine, based on the plea agreement, what level of criminal homicide is appropriate. The plea agreement between Ruelas and the prosecutor stated that the circuit court would consider first-degree murder, second-degree murder, and manslaughter. First-degree murder carried a possible sentence of up to life with no parole; second was life with the opportunity for parole; manslaughter was capped at fifteen years in jail. The circuit court, after ruling out first-degree, found Ruelas guilty of second-degree murder. Ruelas was sentenced to 250 months to 40 years in prison with the possibility of parole.
Ruelas then began a series of challenges to his guilty plea and conviction. These culminated in an attempt to withdraw his plea. The trial court construed his motion to withdraw his plea as a motion for relief from judgment and denied it. Ruelas argued first that the circuit court never mentioned manslaughter when it found him guilty of second-degree murder, and, second, that at the time Ruelas pleaded to and was found guilty of second-degree murder, manslaughter could not have been considered during an "open murder" hearing under Michigan law. Ruelas argued that this rendered his plea involuntary because he thought he had a shot of being found guilty of merely manslaughter.
The state courts denied this claim, finding that his plea was not involuntary and, even if it was, any such error was "harmless." Ruelas then filed a petition for a writ of habeas corpus in federal court, alleging (among other things), that his plea was unknowing and involuntary and that his guilty plea must be vacated as a result. Ruelas does not argue that someone else killed his mother; he argues that the highest charge sustainable against him is manslaughter. Br. of Petitioner/Appellee at 12. The district court rejected most of Ruelas's arguments but agreed that his guilty plea was improper and further that this defect had a substantial and injurious effect on his conviction. The district court granted the writ because it concluded that Ruelas was likely to have pleaded innocent if he had known he was ineligible for manslaughter, and therefore he was entitled to habeas relief. Michigan appeals.

II.
Two minor points must be cleared up before addressing the merits. First, Michigan argues that, though Ruelas otherwise exhausted his state remedies before filing his habeas petition, we should nevertheless dismiss his claim as unexhausted because there is a chance that, were he to file a new motion in state court, Michigan's courts might change the law and allow his petition to proceed. Specifically, Michigan argues that, were we to dismiss Ruelas's case, the Michigan courts might find the Supreme Court's decision in Castro v. United States, 540 U.S. 375, 124 S.Ct. 786, *407 157 L.Ed.2d 778 (2003) persuasive. In Castro, the Court held that if a court construes a pro se petitioner's motion to have been asserted under a ground different than the one stated, the re-styled motion only counts as a "first" petition under 28 U.S.C. § 2255, if the pro se petitioner was warned that the re-styled motion would have preclusive effect. Id. at 383-84, 124 S.Ct. 786. It is a sound rule.
But no Michigan court has ever cited Castro, and, being grounded in the Court's supervisory power over lower federal courts, it is not directly binding on them. Id. at 382-84, 124 S.Ct. 786. Michigan's Attorney General argues, nevertheless, that Michigan's courts will surely see Castro's wisdom, and thus this Court should dismiss Ruelas's claim and give them the opportunity to see if they want to adopt the rule for themselves. The AG further assures us that, if we took this action, he would argue for, not against, adoption of the Castro rule, even though that would be against the state's interests at that point. Suffice to say that we cannot accept that argument. It is wholly speculative whether Michigan would adopt the Castro rule, as it is under no compulsion to do so. And we do not even know if Ruelas's claim would properly fit within itRuelas's motion to withdraw was re-styled as a motion for relief from judgment, but Michigan would have to delineate the contours of its own Castro rule based on Michigan procedure, of which this Court cannot claim any expertise. Moreover, dismissing Ruelas's case for this reason would suggest to Michigan's courts that they must adopt the Castro rulethat we were strong-arming them into adopting it because we, as federal judges, think it is a good idea. Yet that is for Michigan to decide. The state courts did not adopt the rule the first time Ruelas filed for relief, and there is little reason for us to think they have changed their minds. In any event, even if we take the Attorney General's offer as one made in good faith, it is not to our knowledge enforceable, and it is not for us to force that office's hand in a later stage of litigation, wholly apart from federal court. It is best for us to stay out of that speculative game. We hold that Ruelas exhausted his state court remedies, and that this appeal is properly before us.
Second, after the district court granted judgment in favor of Ruelas on his involuntary guilty plea claim, Michigan filed a motion for relief from judgment under Federal Rule of Civil Procedure 60(b). Michigan then appealed this case to this Court two days later, and then re-filed its 60(b) motion with the district court. That motion sought an evidentiary hearing into whether Ruelas's plea was voluntary, and the state submitted affidavits from the trial prosecutor and defense counsel. The district court has not yet acted on this 60(b) motion.
In its brief in this case, Michigan improperly relies on evidence it submitted when it filed its 60(b) motion. This evidence is not properly before us. First, the district court correctly did not rule on the 60(b) motion while this appeal remained pending, as it lost jurisdiction over it: "After an appeal of a trial court's final judgment has been perfected by the filing of a notice of appeal, the trial court no longer has jurisdiction to grant a Rule 60(b) motion." Pickens v. Howes, 549 F.3d 377, 381 (6th Cir.2008). The district was free, however, to "indicate that it would grant the motion," which would allow the appellant to "make a motion in this court for a remand of the case so that the district court c[ould] grant relief." Id. at 383 (quoting Bovee v. Coopers & Lybrand C.P.A., 272 F.3d 356, 359 n. 1 (6th Cir. 2001)). That did not happen here, and in any event, the grant of appeal in this case rendered the 60(b) motionand any evidence attached thereto that was not part *408 of this appealirrelevant to this case. Parties may not rely on evidence outside of the record, and that includes the evidence Michigan submitted with their 60(b) motion, which, as explained above, is treated as an entirely separate proceeding. Thus, because those documents were never introduced to either the state courts nor to the district court in this case, we may not consult those documents. And, for the reasons explained below, we do not need to consult that evidence to resolve this case.

III.
On a federal habeas appeal from a state court judgment, we review a district court's legal conclusions and mixed questions of law and fact de novo, and we review its factual findings for clear error. Armstrong v. Morgan, 372 F.3d 778, 781 (6th Cir.2004); Lucas v. O'Dea, 179 F.3d 412, 416 (6th Cir.1999). Under the Antiterrorism and Effective Death Penalty Act of 1996, a federal court may not set aside a state judgment sustaining a prisoner's conviction without finding that the decision (1) is "contrary to," or an "unreasonable application" of, "clearly established federal law," or (2) was based on an "unreasonable determination of the facts in light of the evidence presented" to the state courts. 28 U.S.C. § 2254(d). A state court decision is "contrary to" established federal law if the state court arrived at a conclusion opposite to one reached by the Supreme Court on a question of law or if it decides a case differently than the Supreme Court on materially indistinguishable facts. Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court "unreasonably applied" clearly established federal law if it identified the correct legal principle but unreasonably applied that standard to the facts of the prisoner's case. Id. at 413, 120 S.Ct. 1495. And although "clearly established federal law" in § 2254(d)(1) simply "refers to the holdings" of the Supreme Court, courts may look to the lower courts of appeals' decisions to inform the analysis of Supreme Court holdings in determining whether a legal principle has been clearly established by the Supreme Court. Hereford v. Warren, 536 F.3d 523, 528 (6th Cir.2008) (citing Hill v. Hofbauer, 337 F.3d 706, 716 (6th Cir.2003)).

IV.
A defendant who pleads guilty waives a number of federal constitutional rights, including the right to a jury trial and the right to confront his accusers. Boykin v. Alabama, 395 U.S. 238, 243, 89 S.Ct. 1709, 23 L.Ed.2d 274 (1969). Because of the importance of these rights, reviewing courts must ensure that the defendant's waiver was knowing and voluntary. We therefore insist that the defendant appreciated the consequences of the waiver, did so without coercion, and understood the rights surrendered. Brady v. United States, 397 U.S. 742, 748-50, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970); Fautenberry v. Mitchell, 515 F.3d 614, 636-37 (6th Cir.2008). Specifically, guilty pleas "not only must be voluntary but must be knowing, intelligent acts done with sufficient awareness of the relevant circumstances and likely consequences." Brady, 397 U.S. at 748, 90 S.Ct. 1463. The Supreme Court defines a voluntary plea as one "entered by one fully aware of the direct consequences." Id. at 755, 90 S.Ct. 1463.
While a defendant need not know all the possible consequences of his plea, like the loss of his right to vote or own a gun, or the effect on future sentence, he must be aware of the maximum sentence to which he is exposed. King v. Dutton, 17 F.3d 151, 154 (6th Cir.1994); Hart v. Marion Corr. Inst., 927 F.2d 256, 259 (6th Cir.1991). And, "[a]t a minimum, the defendant must understand the `critical' or *409 `essential' elements of the offense to which he or she pleads guilty." United States v. Valdez, 362 F.3d 903, 909 (6th Cir.2004) (citing Bousley v. United States, 523 U.S. 614, 618-19, 118 S.Ct. 1604, 140 L.Ed.2d 828 (1998)). The satisfaction of these requirements cannot be inferred from the bare fact that the defendant pleaded guilty, because he still might not have known what he was giving up when he did so. Boykin, 395 U.S. at 243, 89 S.Ct. 1709.
Ruelas argues that his guilty plea was invalid because, contrary to the plea's terms, manslaughter was not a permissible option during his "open murder hearing" under then-applicable Michigan law. (The law has since changed: were Ruelas to plead guilty to "open murder" today, manslaughter could be considered.) He argues that his plea was thus "involuntary" and that he should be permitted to withdraw it. In support, Ruelas contends both that Michigan law forbade manslaughter from being imposed, so the guilty plea should be held invalid on some kind of mutual mistake theory, and further that the circuit court never discussed manslaughter during his degree hearing, instead concluding that second-degree murder applied after ruling out first-degree murder. But things are not quite so simple.
Michigan law was in flux when Ruelas pleaded guilty. It was not clear whether manslaughter was a lesser included offense of murderand thus could be considered during an "open murder" hearingor was not. Plea agreements may be held invalid if prosecutors, defense counsel, and the court are confused or mistaken as to the law, Bousley, 523 U.S. at 618-19, 118 S.Ct. 1604, and so, Ruelas argues, his plea was invalid because the judge at his degree hearing was compelled by law to ignore manslaughter, contra to his plea. But maybe not: our Court has explained, under Michigan law in effect during this period, that "[i]f, based on the evidence adduced at the [degree] hearing, the trial judge determine[d] that a conviction for manslaughter but not murder [wa]s warranted, the trial judge is required to refuse to accept the plea of guilty to the charge of murder[.]" Berry v. Mintzes, 726 F.2d 1142, 1144 (6th Cir.1984) (citing People v. Middleton, 22 Mich.App. 694, 177 N.W.2d 652 (1970)). So it is possible that manslaughter was still on the table as a practical matter, the only difference being that the judge was required to take the extra step of refusing the plea and institute a manslaughter conviction, rather than to do so directly and under the plea agreement. In any event, Michigan appears to have outgrown this temporary oddity and now manslaughter may be considered under an open murder plea because it is considered a "lesser included" or "inferior" crime to murder. People v. Mendoza, 468 Mich. 527, 664 N.W.2d 685, 694 (2003).
Yet, even if we assume that Michigan law forbade the circuit court from considering manslaughter, it is ambiguous what it in fact considered; if it did consider manslaughter, even if that was contrary to the law at the time, then it is not clear what Ruelas lost. Indeed, the circuit court simply never used the word manslaughter, stating only:
The Court could not find any specific intent in this case. The Court could not find a premeditated murder. And so, murder one is out. But, I do think that murder two was well demonstrated. The Defendant did great bodily harm to the victim knowing that he created a high risk of death, or great bodily harm knowing that death from such harm would like result [from] his actions. And so, the Court does make a finding [that] Mr. Ruelas is guilty of second-degree murder under the laws of this State.
*410 It explained that it was sentencing Ruelas to second-degree rather than first-degree murder because he lacked premeditation. Ruelas argues, however, that the court's failure to distinguish manslaughter from second-degree murder, which the court found him guilty of, indicated that manslaughter was not considered. Yet, under Michigan law, the difference between second-degree murder and manslaughter is that a manslaughter conviction requires the defendant to show, by a preponderance of the evidence, that he killed in the "heat of passion," with such passion caused by "adequate provocation," without "a lapse of time during which a reasonable person could control his actions." Mendoza, 664 N.W.2d at 690. Moreover, the presence of provocation was something Ruelas was required to prove, and the fact that the circuit court did not mention manslaughter does not automatically mean that it did not consider it; Ruelas offers little evidence of provocation.
The final sticky point is, even assuming that the judge could not consider manslaughter, whether that is legally sufficient to render his plea involuntary. On one hand, courts have focused on whether the defendant was aware of the maximum possible sentence, not the minimum. Dutton, 17 F.3d at 154. On the other, "plea bargains are essentially contracts[,]" Puckett v. United States, ___ U.S. ___, ___, 129 S.Ct. 1423, 1430, 173 L.Ed.2d 266 (2009), and courts have long set those aside where the parties (here, the prosecutors and defendant), made a "mutual mistake," e.g., Raffles v. Wichelhaus, 2 H. & C. 906 (Ex. 1864). Extending that reasoning here would mean that the plea was invalid because both sides did not know what they were bargaining for, as one of the plea's key elementsRuelas's shot at getting only manslaughterwas not actually on the table. The district court did not discuss these concerns, and merely assumed that if Michigan could not sentence Ruelas to manslaughter then a violation occurred.
But we need not resolve these conundrumsboth factual and legalbecause the simplest way to resolve this case is to assume that Michigan either could not or did not consider manslaughter, and to further assume such error rendered Ruelas's guilty plea involuntary. We thus assume a constitutional violation, so the question is whether that violation was harmless or not.

V.

A.
Ruelas argues that a finding that his guilty plea was involuntary ought to end his case because all such errors are "structural." "Structural errors" are those that "defy" analysis by normal harmless error standards, Arizona v. Fulminante, 499 U.S. 279, 309, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991), because their consequences "are necessarily unquantifiable and indeterminate," so reversal is "automatic." United States v. Gonzalez-Lopez, 548 U.S. 140, 150, 126 S.Ct. 2557, 165 L.Ed.2d 409 (2006). Ruelas's case, however, neither "defies" harmless error standards nor is the harm "unquantifiable and indeterminate." His argument otherwise relies on a faulty premise: that the remedy for all involuntary guilty pleas is the right to go back, plead innocent, and have a trial. That is sometimes the remedy, but not always, and not here. Habeas courts have "broad discretion" in crafting remedies for constitutional errors. See Pickens, 549 F.3d at 382. And, because guilty pleas are in the nature of contracts, Puckett, 129 S.Ct. at 1430, the remedy for Ruelas is specific performance of what he bargained for: a degree hearing where first-degree murder, second-degree murder, and manslaughter could all be considered. *411 E.g., Pickens, 549 F.3d at 382 ("[W]e hold that it is unnecessary to permit a person to withdraw an illegal plea or require the state to retry a case when the defendant's sentence has been modified to make the sentence legal and to give the defendant every benefit of his bargain.").[1] Here, the "benefit of the bargain" is the opportunity to be considered for manslaughter, and that is the sort of analysis judges can perform during a harmless-error inquiry. So in this case, where Ruelas pleaded to "open murder" under Michigan law, we can apply harmless error standards to determine whether the Michigan courts properly concluded that he was guilty of second-degree murder. The assumed error was not "structural."

B.
Determining whether an error is harmless on habeas review requires us to ask whether the error "had [a] substantial and injurious effect or influence in determining the jury's verdict." Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)). In this Circuit, Brecht is the standard for reviewing all (non-structural) errors on collateral review; it applies "whether or not the state appellate courts recognized the error." Vasquez v. Jones, 496 F.3d 564, 575 (6th Cir.2007) (citing Fry v. Pliler, 551 U.S. 112, 117-18, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007)). In Fry, the Supreme Court rejected the petitioner's argument that the "harmless beyond a reasonable doubt" standard of Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967) is appropriate on collateral review if the state court did not engage in a harmless error analysis. The Court held that habeas petitioners are not guaranteed one bite at the Chapman apple, and instead ruled that the Brecht standard flowed from principles of comity, federalism, and deference to state courts, and therefore applied on habeas review, Fry, 551 U.S. at 117-18, 127 S.Ct. 2321.
The Fry Court also observed that post-Brecht developments (namely, the passage of the AEDPA) did not undermine Brecht, and that standard continues to apply today. Id. at 119-20, 127 S.Ct. 2321. Yet the interplay of Brecht and the AEDPA is not always straightforward. Here, the state courts first held that no constitutional violation occurred, but then also intimated that, even if Ruelas's plea had been unconstitutional, any error was non-prejudicial, though they did not discuss the issue at length or even cite Chapman. From experience, this is typical: state courts, in reviewing claims of prisoners, tend to state in their opinions, "Petitioner's claim of constitutional error fails on the merits, and, alternatively, any error would have been harmless." That the rulings in Brecht and Fry did not take this form was something of a fluke. The question then is: How does a federal habeas court review the decision of a state court that decided a constitutional error was harmless? Or when it is ambiguous if they performed such review at all? It will be recalled that, on habeas review, state court constitutional rulingsand Chapman was *412 a constitutional caseare reversible only if the state decision was "contrary to" or an "unreasonable application of" clearly established federal law. 28 U.S.C § 2254(d)(1).
The answer in this Circuit is that Brecht is always the test, and there is no reason to ask both whether the state court "unreasonably" applied Chapman under the AEDPA and, further, whether the constitutional error had a "substantial and injurious" effect on the jury's verdict. See, e.g., Hall v. Vasbinder, 563 F.3d 222, 236 (6th Cir.2009); Fleming v. Metrish, 556 F.3d 520, 537 (6th Cir.2009); Vasquez, 496 F.3d at 575. In coming to that conclusion, we take guidance from a passage in Fry stating that "it certainly makes no sense to require formal application of both tests (AEDPA/Chapman and Brecht) when the latter obviously subsumes the former." 551 U.S. at 120, 127 S.Ct. 2321. In other words, the determination of whether an error had a "substantially injurious" effect on the jury's verdict is broader and thus "subsumes" the question whether the state court reasonably applied Chapman. Before Fry was handed down, this issue had caused much consternation in the lower courts (including this one),[2] but the Supreme Court made clear its view with this passage in Fry (though the issue had not been heavily briefed, taking up but a single footnote in the Solicitor General's brief): Fry held that Brecht applies to all cases on collateral review, and a federal habeas court is never required to determine whether a state court's harmless error determination was "unreasonable"Brecht handles the work on this, too.
Yet one of our sister circuits recently held otherwise. In Johnson v. Acevedo, 572 F.3d 398 (7th Cir.2009), the Seventh Circuit held that habeas courts must always go through a two-step process: "If the state court has conducted a harmless-error analysis, the federal court must decide whether that analysis was a reasonable application of the Chapman standard. If the answer is yes, then the federal case is over.... If the answer is no ... then § 2254(d) drops out of the picture and the federal court must" apply the Brecht test. Id. at 404. The Seventh Circuit relied on Mitchell v. Esparza, 540 U.S. 12, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003) (per curiam), to support this formulation. In Esparza, the Court held that a panel of this Circuit improperly applied the AEDPA when it failed to ask if a state court's determination that a constitutional error was unreasonable rather than simply incorrect. Id. at 16-17, 124 S.Ct. 7.
Although we agree with the Seventh Circuit that "Fry did not overrule Esparza," Johnson, 572 F.3d at 404, the two cases may be harmonized more simply than does the Seventh Circuit. We believe the Johnson court misreads Esparza insofar as it thinks that courts must always go through this two-step inquiry. Of course, Esparza says that if a state court's harmless error determination was reasonable, then a federal court has no authority to grant the writ. But in Fry the Justices also told us that Brecht's "substantially injurious" test "obviously subsumes" the question whether Chapman was reasonably applied: How could the determination *413 that something was harmless beyond a reasonable doubt be unreasonable if it did not also have a "substantially injurious" effect on the jury? Moreover, because "it certainly makes no sense to require formal application of both tests (AEDPA/ Chapman and Brecht)," Fry, 551 U.S. at 120, 127 S.Ct. 2321, Fry, as a practical matter, "subsumes" Esparza. But again: Esparza was not overruled. Per that case, a habeas court remains free to, before turning to Brecht, inquire whether the state court's Chapman analysis was reasonable. If it was reasonable, the case is over. But in Fry the Justices also emphatically stated (there was no dissent regarding this point), that a habeas court may go straight to Brecht with full confidence that the AEDPA's stringent standards will also be satisfied.

C.
So the Brecht test applies. Ruelas flunks it. Assuming that the state courts unreasonably applied federal law in determining that Ruelas's plea was not improper, the inquiry becomes whether the circuit court's failure to consider manslaughter "had a substantial and injurious effect or influence" on the determination that he was guilty of second-degree murder. Brecht, 507 U.S. at 623, 113 S.Ct. 1710. In other words, the question is whether Ruelas was prejudiced such that he lost a legitimate chance to be sentenced to manslaughter rather than second-degree murder. The burden for showing an error to be harmless is on the government, O'Neal v. McAninch, 513 U.S. 432, 436, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995), though on habeas review judges independently review the facts supporting the judgment themselves; but the scale, if equal, tips in favor of the defendant, id. at 435-36, 115 S.Ct. 992.
In Michigan second-degree murder requires the government to prove that there was (1) a "death, (2) caused by the defendant's act," (3) the act was done "with malice, and (4) without justification." Mendoza, 664 N.W.2d at 689. The "malice" required by second-degree murder is (1) an "intent to kill," (2) an "intent to cause great bodily harm," or (3) an "intent to do an act in wanton and willful disregard" of a high chance that it would "cause death or great bodily harm." People v. Goecke, 457 Mich. 442, 579 N.W.2d 868, 878 (1998). The only difference between second-degree murder and manslaughter is the "malice" element (first-degree murder differs from second in that it requires premeditation). A defendant is guilty only of manslaughter if he "killed in the heat of passion, the passion was caused by adequate provocation, and there was not a lapse of time during which a reasonable person could control his passions." Mendoza, 664 N.W.2d at 690. Although the government must prove harmless error and the state must always prove its case beyond a reasonable doubtthe burden of proof to show provocation, however, is on the defendant, and it must be shown by a preponderance of the evidence. People v. Darden, 585 N.W.2d 27, 31 (Mich.Ct.App. 1998) ("Provocation, or the absence of provocation, is not an element of the prosecutor's case.").
Ruelas's only support for his contention that he merited only manslaughter and not second-degree murder, was that his mother provoked him when she slapped him across the face and told him not to refer to his ex-wife as a "bitch." J.A. 217. This is not powerful evidence. Moreover, that the circuit court, at the degree-hearing, did not explicitly "rule out" manslaughter is of no moment because it was not the government's burden to prove it. And, we believe, had the judge considered manslaughter at Ruelas's degree hearing, he would have still been found guilty of second-degree murder because he proffered no *414 evidence establishing sufficient "provocation" under Michigan law. As a result, the failure to consider manslaughter did not have a substantial and injurious effect on Ruelas's chance of receiving a manslaughter charge, as the charge of second-degree murder was well supported and Ruelas offered little evidence of provocation.

VI.
For the above reasons, we REVERSE the district court's judgment and vacate the order to issue the conditional writ of habeas corpus.
NOTES
[*]  The Honorable Michael H. Watson, United States District Judge for the Southern District of Ohio, sitting by designation.
[1]  Ruelas also relies on the supposed semantic distinction between "structural" and "trial errors," arguing that because there was no trial in this case, the error must be structural. That does not follow. While it is true that errors susceptible to normal harmless error analysis are often colloquially referred to as "trial errors," see, e.g., Hedgpeth v. Pulido, ___ U.S. ___, ___, 129 S.Ct. 530, 532, 172 L.Ed.2d 388 (2008); Neder v. United States, 527 U.S. 1, 15, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999), the gravamen of the "structural error" inquiry is whether the error "defies" harmless-error analysis, and, for the reasons given above, the error here does not meet that test.
[2]  Compare Eddleman v. McKee, 471 F.3d 576, 583 (6th Cir.2006) ("AEDPA replaced the Brecht standard with the standard of Chapman plus AEDPA deference when ... a state court made a harmless-error determination."); Gutierrez v. McGinnis, 389 F.3d 300, 306 (2d Cir.2004) ("The Supreme Court implicitly rejected Brecht as the proper lens for examining the harmlessness of constitutional errors on collateral review, at least where the state explicitly adjudicated a federal claim on harmless error grounds."); with Inthavong v. LaMarque, 420 F.3d 1055, 1061 (9th Cir. 2005) ("[B]oth the Brecht and the AEDPA/ Esparza tests must be satisfied with respect to harmless error before relief can be granted.").
