Petitioner-appellee Adolf Carter (“Carter”) was convicted of murder and armed violence in Illinois state court following a jury trial. Carter challenges the murder conviction, contending that instructions given his jury violated his federal- due process rights. George E. DeTella, the Warden of Danville Correctional Center where Carter is incarcerated, appeals from a judgment of the district court granting Carter’s petition for a writ of habeas corpus.1 We reverse.
I. BACKGROUND
A Facts
John Young (“Young”) testified that he was with some friends on October 5, 1985, around 8:00 or 8:30 p.m. when he spoke with James Bates (“Bates”) and his girlfriend Giselle Byrd (“Byrd”) on a Chicago street. Bates asked Young to take them to the south side of the city in his car. William Johnson and Debra Young were in the back seat of Young’s car; Young told Byrd to sit in the front seat with Bates. As Young was about to enter the driver’s seat, Bates was also getting ready to enter the car’s front seat on the passenger side. Young heard a noise and saw Bates fall. Young stepped out of the car to go help Bates, and Carter was standing with a baseball bat near the back of the car. Bates was lying on the ground next to the car, and Carter was standing over him. Bates slowly used his hands to try to get up. Carter told Byrd to get out of the ear, and *1387she slammed the car door closed. As Bates was trying to get up, Carter hit him in the head with the bat. Carter then left, and Young drove Bates to the hospital.
When Bates went home from the hospital later that evening, he was complaining that his head hurt; his mother watched over him. She went to work early the next morning, and then Byrd watched him. At one point she dozed off, and when she awoke, Bates was dead.
Byrd testified that she had just gotten into Young’s car, and Bates was ready to get in when he fell. She looked outside the car and saw Carter standing with a baseball bat. Carter said, “[bjitch, you get out, I’m going to get you, too.” Tr. at 257. Byrd did not close the door because Bates’ foot was in it; she never closed the door during the incident. Carter then swung the bat and hit Bates while he was on the ground, and then ran.
Byrd testified that two days before, she was with her brother, William Byrd (“William”), Bates, Carter, and Wayne Bay (“Bay”), one of Carter’s friends. The four men got into a fight because Carter accused Byrd of arguing in front of his mother’s house, when Byrd was not there. At one point, Carter tried to hit Bates with a bottle. Bay pulled a knife, and William kicked it away. When asked if Carter got stabbed, Byrd answered, “I don’t know. I doubt it.” Id. at 290.
William Johnson (“Johnson”) testified that he was sitting in the back seat of the passenger side of Young’s ear, talking with Young, Byrd, and Debra Young for about five minutes before Bates started to get into the car.2 As Bates was getting into the car, he was hit on the top of his head with a bat and fell. Johnson looked out the side window and saw Carter standing with a bat; Carter was telling Byrd to get out of the car. As Bates tried to get up from the ground, Carter hit him on the head with the bat. Byrd then started crying and screaming and locking the doors. Carter ran off.
Carter testified that on the night of the incident, as he was walking from his house to the store, he passed Byrd and Young on the street. Byrd approached him in the store, and told Carter she wanted to talk to him. Carter said they didn’t have anything to talk about, and left the store. Byrd followed him, and told him she had been drunk and was sorry that the fight two days earlier had happened. Carter testified that he was stabbed in the leg and knocked down during the fight.
Carter was talking to Byrd on the sidewalk and Young was standing by the back of his car. As Byrd was talking to Carter, she “threw her hand[s] over her face.” Id. at 452. Carter was seared, because he had fought -with the same people two nights before, and he dropped to the ground. He was about six or seven feet from the car. Carter heard a noise close by and from behind. When he turned around, he saw Bates holding a bat about five feet away. Carter was scared, and thought that Bates had tried to hit him with the bat. Carter got up and ran into Bates, they started to wrestle, fell, and Carter got hold of the bat and hit Bates on the head with it. Carter testified that he struck Bates because he believed that Bates was trying to kill him. Byrd and Young were still present. Byrd ran to the car, and Carter told her to get out, believing she had set him up. He then talked to Young, and left.
The medical examiner who performed the autopsy on Bates testified that there was extensive hemorrhaging under the scalp, an extensive skull fracture, and injury to the brain. Bates’ death “was caused by multiple blunt trauma injuries to the head.” Id. at 373. The injuries were consistent with a person being struck on the head more than once with a bat, but not with someone hitting his head on the sidewalk.
B. Jury Instructions
Carter’s jury was given the then current Illinois Pattern Jury Instructions on murder and voluntary manslaughter based on an un*1388reasonable belief of justification.3 Ill.Pattern Jury Instructions, Criminal IPI, No. 7.02 (“Issues in Murder”) and No. 7.06 (“Issues in Voluntary Manslaughter — Intentional—Belief of Justification”) (2d ed. 1981). The jury was also instructed on self-defense4 and armed violence.
The murder instruction listed the elements of murder and told the jury that the State must prove them beyond a reasonable doubt. The voluntary manslaughter instruction listed the elements of voluntary manslaughter and told the jury that the State must prove them beyond a reasonable doubt. The elements of voluntary manslaughter include all the elements of murder (except for murder while committing an offense), and also include the element (in Carter’s case) that defendant acted under an unreasonable belief that circumstances existed which would have justified the killing (sometimes referred to as “mitigating” because, in a sense, it is a defense to murder).5 The jury was not told that it could not convict of murder unless the State disproved the mitigating element beyond a reasonable doubt.
These instructions are the same as those considered in People v. Reddick, 123 Ill.2d 184, 122 Ill.Dec. 1, 526 N.E.2d 141 (1988), and Falconer v. Lane, 905 F.2d 1129, 1136 (7th Cir.1990), except that in those cases the jury was also instructed on voluntary manslaughter based on serious provocation; that instruction placed the burden on the State to prove that the defendant acted under a sudden and intense passion resulting from serious provocation by another.
In Reddick, the Illinois Supreme Court held that when these murder and voluntary manslaughter instructions are given without warning the jury that it could not convict of murder unless the State disproved the mitigating elements, they “erroneously state the burdens of proof on the issues of whether the defendants acted under either intense passions or unreasonable beliefs that their actions were justified.” 122 Ill.Dec. at 5, 526 N.E.2d at 145. “These instructions essentially assure that, if the jury follows them, the jury cannot possibly convict a defendant of voluntary manslaughter. The reason is that even if a mitigating mental state is proved, it will have been proved by the defendant, not the People.” Id. The court concluded that “grave error” had occurred. Id., 122 Ill.Dec. at 7, 526 N.E.2d at 147.6
Subsequently, this court held that when the same instructions are given, they violate federal due process because a jury may have been left with the false impression that it could convict of murder even if there was a mitigating mental state. Falconer, 905 F.2d at 1136; see also Verdin v. O’Leary, 972 F.2d 1467, 1470 (7th Cir.1992); Flowers v. Ill. Dep’t of Corrections, 962 F.2d 703, 705 (7th Cir.1992), vacated on other grounds, — U.S. —, 113 S.Ct. 2954, 125 L.Ed.2d 656 (1993), on remand, 5 F.3d 1021 (1993); Taylor v. Gilmore, 954 F.2d 441, 450 (7th Cir.1992), rev’d on other grounds, — U.S. —, 113 *1389S.Ct. 2112, 124 L.Ed.2d 306 (1993), on remand, 4 F.3d 997 (1993) (Table); United States ex rel. Fleming v. Huch, 924 F.2d 679, 682 (7th Cir.1991); Rose v. Lane, 910 F.2d 400, 402 (7th Cir.), cert. denied, 498 U.S. 983, 111 S.Ct. 615, 112 L.Ed.2d 526 (1990).
C. Procedural History
In an unpublished opinion (following a petition for rehearing by Carter), the Illinois Appellate Court found that while the instructions were error under Reddick, the error was harmless because “the evidence of defendant’s guilt in this case is so clear and convincing that a jury could not reasonably have found defendant not guilty of murder and guilty only of voluntary manslaughter based on an unreasonable belief of justification.” Nov. 27, 1989 Order at 7. The Illinois Supreme Court denied Carter’s petition for leave to appeal.
Subsequently, Carter filed a petition for a writ of habeas corpus in federal district court. The district court granted Carter’s petition, finding that the instructions violated both Illinois and federal constitutional law, and that the error “ ‘so infected the trial as to violate due process’” because, in part, “[t]he jury could well have reached that result [conviction of voluntary manslaughter] if it believed in large measure the defendant’s testimony and disbelieved the state’s witnesses.” July 10,1992 Mem. and Order at 10,11. The State filed a motion to amend the judgment, which the district court denied (except as to a ministerial change not at issue). The State now appeals.
II. DISCUSSION
A. Fair Presentment
In United States ex rel. Spurlark v. Wolff, 699 F.2d 354 (7th Cir.1983), this court held that a state prisoner seeking habeas relief is barred from raising a claim he had failed to raise on a state court appeal, unless he can show cause and prejudice. See Murray v. Carrier, 477 U.S. 478, 489-490, 106 S.Ct. 2639, 2646-2647, 91 L.Ed.2d 397 (1986). A petitioner’s claim “must have been presented in such a way as to fairly alert the state court to any applicable [federal] constitutional grounds for the claim.” United States ex rel. Sullivan v. Fairman, 731 F.2d 450, 453 (7th Cir.1984).7
Earlier, in the context of exhaustion of state remedies, the Supreme Court had said that “the federal claim must be fairly presented to the state courts.” Picard v. Connor, 404 U.S. 270, 275, 92 S.Ct. 509, 512, 30 L.Ed.2d 438 (1971). “[W]e do not imply that respondent could have raised ... [his federal constitutional] claim only by citing ‘book and verse on the federal constitution.’ ... [citations omitted]. We simply hold that the substance of a federal habeas corpus claim must first be presented to the state courts.” Id. at 278, 92 S.Ct. at 513.
In Taylor v. Gilmore, decided after Falconer, this court ruled that Reddick was grounded only in state law, with no ties to federal due process; “[a]ny indications to the contrary in our prior decisions are disavowed.” 8 954 F.2d at 449.
*1390In Verdin v. O’Leary, a habeas petitioner claimed that the Illinois Pattern Jury Instructions violated the Due Process Clause because they had led “the jury to ignore constitutionally relevant, exculpatory evidence.” 972 F.2d 1467, 1477 (7th Cir.1992). In state court he had not expressly claimed a violation of due process, but had argued that a refused instruction was necessary for the jury to understand the difference between murder and voluntary manslaughter. He only cited to state cases, none of which refer to the Due Process Clause or cite cases referring to the Due Process Clause. The State likewise did not refer to the Due Process Clause, and the appellate court did not reference constitutional grounds. This court concluded that there had been no fair presentment of his federal claim, and remanded to the district court to determine whether the petitioner’s waiver of his federal claim could be excused under the “cause and prejudice” test or whether failure to consider his federal claim would result in a fundamental miscarriage of justice. Id. at 1483.
On direct appeal, in a supplemental brief to the Illinois Appellate Court,9 Carter argued that the instructions were error under Reddick.10 In its supplemental response brief, in the context of retroactivity, the State argued that Reddick is not of constitutional magnitude, and therefore should not be applied retroactively. In his supplemental reply brief, with respect to the State’s retroac-tivity argument, Carter stated that “the present rule is Constitutional,” the “instructions on murder violate the ‘long-established constitutional’ principle recognized in Reddick,” and the “instructions on murder and voluntary manslaughter violate the constitutional right to present a defense and to have a fair trial.” Carter’s Appellate Supplemental Reply Br. at 5-6.
The appellate court’s initial decision did not address the Reddick issue. Carter filed a petition for rehearing, asking the court to find a Reddick error. While the court agreed that there had been a Reddick error, it found the error harmless.
In Carter’s petition for leave to appeal to the Illinois Supreme Court, he argued that the appellate court incorrectly concluded that the Reddick error was harmless, citing only Illinois law.11 The Illinois Supreme Court denied the petition.
Carter subsequently filed a petition for a writ of habeas corpus in federal district court. The State filed its answer to Carter’s petition and memorandum in opposition to the petition on July 12, 1991. The district court granted Carter’s petition on July 10, 1992. The State filed a motion to alter or amend the judgment on July 27, 1992, which the district court denied.
The State admits that ordinarily, it would have been held to have waived the argument that Carter did not fairly present his federal claim because it did not raise the argument below. The State asserts that its failure can be excused because at the time of its briefing in the district court, there was no reason to argue that Reddick was not based on federal constitutional grounds. The State rests this assertion on the ground that because of language in Falconer (see n. 12), it felt that it could not have raised its fair presentment argument until after Verdin v. O’Leary, 972 F.2d 1467 (7th Cir.1992). We note that the state did make a presentment argument in Verdin. Additionally, in Taylor v. Gilmore, this court ruled that Reddick was grounded only in state law, with no ties to federal due process. Taylor, 954 F.2d at 449 (7th Cir.1992). Taylor was decided almost six months before the district court ruled on Carter’s petition.
*1391We need not, however, determine whether Carter adequately presented his federal claim on direct appeal or whether the State waived its presentment argument, given the following discussion.
B. Harmless Error
Carter would like us to read Falconer broadly, as holding that when these murder and voluntary manslaughter instructions are given without alerting the jury to the need to determine whether the mitigating circumstance of an unreasonable belief of justification was present, and if present not to convict of murder, and the jury convicts of murder, there is always a denial of federal due process, and never harmless error, no matter how slight the evidence of an unreasonable belief of justification.12
Several considerations militate against so broad a reading. First, the court in Falconer spoke in terms of a possibility that a jury would improperly convict of murder, and suggested that there was substantial evidence that the defendant, who attempted to prove that she killed in self-defense, did have a mitigating mental state:
The central point is that the jury might have decided to convict the petitioner of murder because the State proved that she intentionally killed another without a reasonable belief that she acted in self-defense—despite clear proof that the petitioner was provoked to murderous passion by the victim or that the petitioner held an unreasonable belief that she was justified in killing the victim.
Falconer, 905 F.2d at 1136 (emphasis added).
Additionally, even though in several cases we have noted the “inherently prejudicial” nature of the instructions,13 all subsequent decisions of this court which have found Falconer-type denials of due process have considered whether the error was harmless and have evaluated the evidence in order to determine that it was not. See Flowers v. Ill. Dep’t of Corrections, 962 F.2d at 705 (“Our review of the record confirms the state trial judge’s apparent belief, given that he tendered a voluntary manslaughter instruction to the jury, that the evidence presented at trial could support either a voluntary manslaughter verdict or a murder verdict. Consequently, we conclude that the error at Flowers’ trial was not harmless beyond a reasonable doubt ...,” id. at 706); Taylor v. Gilmore, 954 F.2d at 450 (considering “whether the erroneous jury instructions ... were harmless beyond a reasonable doubt,” id. at 454) (“Our review of the record- confirms the trial judge’s belief [“that there was enough evidence in the record to support mitigation to manslaughter”] ...,” id.) (noting that “[h]ad there been insufficient evidence in that regard, the judge would not have been obligated to [give the manslaughter instruction] ...,” id.); United States ex rel. Fleming v. Huch, 924 F.2d 679 (“A closer question than whether the jury instructions violated due process is whether that constitutional violation was harmless beyond a reasonable doubt,” id. at 683) (concluding that because there was “substantial and uncontro-verted” evidence of battered wife syndrome, which was basis for self-defense theory, the instructional error was not harmless, id.); Rose v. Lane, 910 F.2d at 402 (“we must decide ... whether the trial court’s constitutional error was harmless,” id. at 403) (concluding that because there was evidence that the defendant believed he was acting in self-defense, a jury might not have convicted him of murder if properly instructed, id.). Thus, *1392we have interpreted Falconer as permitting consideration of whether Falconer-type errors were harmless in light of the evidence before the jury.
Finally, the Supreme Court has decided that “the Kotteakos harmless-error standard applies in determining whether habeas relief must be granted because of constitutional error of the trial type.” Brecht v. Abrahamson, — U.S. -, -, 113 S.Ct. 1710, 1722, 123 L.Ed.2d 353 (1993).14 There must be more than “a ‘ “reasonable possibility” ’ that trial error contributed to the verdict”; habeas petitioners are entitled to habeas relief based on trial error only if the error resulted in “actual prejudice.” Id. at -, -, 113 S.Ct. at 1721-1722. The question is whether the error “‘had substantial and injurious effect or influence in determining the jury’s verdict.’ ” Id. at-, 113 S.Ct. at 1722 (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 1253, 90 L.Ed. 1557 (1946)).
In contradiction to Carter’s testimony that Bates swung the bat at him (from which follows Carter’s contention that he believed Bates was trying to kill him), three state witnesses testified that Bates was knocked to the ground as he was entering Young’s car, and that Carter hit Bates while Bates was on the ground.15 None of the witnesses saw a conversation between Carter and Byrd, or a struggle over the bat between Bates and Carter. Carter’s testimony that he hit Bates only one time is also contradicted by the autopsy results, which show that Bates was struck more than once.
There are indeed some questions of credibility in deciding the correct version of the facts. We do note that the jury must have found Carter’s version incredible in large part because it rejected the claim that he acted in self-defense. Insofar as possible the habeas or appellate court shuns resolving credibility and weighing the evidence. Nevertheless, the Brecht-Kotteakos test for harmless error requires the habeas court to evaluate to some extent the probability of the outcome if the case were tried under proper instructions.
The constitutional error perceived in Falconer was that “the jury may have been left with the false impression that it could convict the petitioner of murder even if she possessed one of the mitigating states of mind described in the voluntary manslaughter instruction” and that “[jjurors are therefore encouraged by the structure of the instructions to answer ... [the requirements of the murder instruction] first and then move on only if those requirements cannot be met.” Falconer, 905 F.2d at 1136.
The Falconer error is present here. We conclude, however, that the error did not have a “substantial and injurious effect or influence in determining the jury’s verdict” and therefore was harmless.16
If in fact the jury did not credit Carter’s testimony and decided that he did not have an unreasonable belief that the killing was *1393justified in self-defense, the error had no effect on the verdict. Assuming, however, that the instruction caused the jury to believe that it could convict of murder even if Carter had such belief, or without considering whether he did, our review of the trial transcript satisfies us that the jury did not and would not have found that Carter had such belief.
Accordingly, the judgment of the district COUrt ÍS REVERSED.
. Because the Attorney General of Illinois represents Mr. DeTella, we will refer to respondent-appellant as “the State."
. Johnson also testified that Young got into the car about five to ten seconds before Byrd.
. The Illinois statutes regarding murder and voluntary manslaughter were rewritten, effective July 1, 1987, to create the offenses of first degree murder and second degree murder.
. Under the relevant section of the Illinois Code
[a] person is justified in the use of force against another when and to the extent that he reasonably believes that such conduct is necessary to defend himself or another against such other's imminent use of unlawful force. However, he is justified in the use of force which is intended or likely to cause death or great bodily harm only if he reasonably believes that such force is necessary to prevent imminent death or great bodily harm to himself or another, or the commission of a forcible felony.
Ill.Ann.Stat. ch. 38, para. 7-1 (Smith-Hurd 1989). The Illinois Pattern Jury Instruction on self-defense follows the statutory language. Ill. Pattern Jury Instructions, Criminal IPI, No. 24-25.06 ("Use of Force in Defense of a Person”) (2d ed. 1981).
. Under the relevant section of the Illinois Code
[a] person who intentionally or knowingly kills an individual commits voluntary manslaughter if at the time of the killing he believes the circumstances to be such that, if they existed,, would justify or exonerate the killing under the principles stated in Article 7 of this Code [Justifiable Use of Force; Exoneration] [footnote omitted], but his belief is unreasonable.
Ill.Ann.Stat. ch. 38, para. 9-2(b) (Smith-Hurd 1979).
. The Illinois Pattern Jury Instructions were rewritten to conform to Reddick.
. In Sullivan, this court concluded that petitioner waived his right to submit his due process claim in federal court because he did not present his due process argument to the state courts in the context of a federal constitutional claim, he never used the language "due process,” he relied on state cases which refer only to the “interests of justice," and the state appellate court opinion indicated that it discerned no due process implications.
For a list of factors to consider in determining whether a petitioner has fairly presented a federal claim, see Sullivan, 731 F.2d at 454 (including n. 9).
. In Falconer v. Lane, this court had implied that a petitioner's citation to Reddick may constitute a federal constitutional challenge to the Illinois jury instructions, noting that in Reddick, "the Court obviously considered the errors resulting from the invalid instructions to be of constitutional magnitude.” Falconer, 905 F.2d at 1134. The petitioner in Falconer did argue to the Illinois Supreme Court that the instructions deprived her of "due process." The panel in Falconer noted that even if the petitioner’s claim was interpreted as brought under the Illinois Constitution’s Due Process Clause, such a claim would be "functionally identical to a federal claim,” and therefore her federal claim was fairly presented. Id.
Additionally, in Rose v. Lane, a panel of this court stated that “Reddick creates a federal claim through In re Winship [397 U.S. 358, 90 S.Ct. *13901068, 25 L.Ed.2d 368 (1970)]...." Rose, 910 F.2d at 401 n. 1.
. Reddick was decided after Carter’s opening brief to the Illinois Appellate Court.
. Carter did cite a United States Supreme Court case in support of his argument that Reddick should be applied retroactively to his case. This, however, is immaterial to whether Carter presented his claim that the instructions violated his federal due process rights.
.A petitioner’s failure to present his federal claim in a petition for leave to appeal to a state's highest court on direct review may constitute waiver of that issue. See United States ex rel. Bonner v. DeRobertis, 798 F.2d 1062, 1065-66 (7th Cir.1986).
. In Falconer, a panel of this court concluded that "[a]s the Eighth Circuit stated in finding constitutionally faulty jury instructions: ‘Such error [a jury verdict based on an instruction that allows it to convict without properly finding the facts supporting each element of the crime] is not corrected merely because an appellate court, upon review, is satisfied that the jury would have found the essential facts had it been properly instructed. The error cannot be treated as harmless.’ ” 905 F.2d at 1137 (citing United States v. Voss, 787 F.2d 393, 398, cert. denied, 479 U.S. 888, 107 S.Ct. 286, 93 L.Ed.2d 261 (1986)).
. Rose v. Lane, 910 F.2d at 402-403 (noting that Falconer found the instructions to be "gravely erroneous" and "inherently prejudicial”); United States ex rel. Fleming v. Huch, 924 F.2d at 683 (recognizing that Falconer and Rose found that the error was “inherently prejudicial”); Taylor v. Gilmore, 954 F.2d at 454 (recognizing that Falconer, Rose and Fleming found the instructions were "inherently prejudicial”).
.While the issue in Brecht was whether a habe-as petitioner was entitled to relief because the state improperly used his post-Miranda silence for impeachment purposes, the harmless error standard announced in Brecht applies to instructional error. See Libby v. Duval, 19 F.3d 733, 739-740 (1st Cir.1994), cert. denied, - U.S. -, 115 S.Ct. 314, - L.Ed.2d - (1994); Kontakis v. Beyer, 19 F.3d 110, 116 (3d Cir.1994), cert. denied, - U.S. -, 115 S.Ct. 215, - L.Ed.2d - (1994); O'Neal v. Morris, 3 F.3d 143, 145-147 (6th Cir.1993), cert. granted in part, - U.S. -, 114 S.Ct. 1396, 128 L.Ed.2d 70 (1994) (question presented: “Does state have burden of proving constitutional error to be harmless under Brecht v. Abrahamson ?” 62 U.S.L.W. 3680). But see Suniga v. Bunnell, 998 F.2d 664, 667 (9th Cir.1993).
Prior to Brecht, the harmless error standard was whether federal constitutional error “was harmless beyond a reasonable doubt." Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967). We apply Brecht here. See Lockhart v. Fretwell, - U.S. -, -, 113 S.Ct. 838, 844, 122 L.Ed.2d 180 (1993).
. At sentencing, the trial judge noted that "in reality what the evidence disclosed was that by his [Carter’s] own lips he had the victim, Mr. Bates, to his knees and under control, took the bat away from him, what he said, and there is really no need for self-defense or striking of Mr. Bates at that time even under the theory advanced by Mr. Carter and his counsel. The jury-rejected that theory of self-defense. They didn’t believe it, and I must say that I didn’t believe it either.” Tr. at 652.
. The Illinois Appellate Court also found that the instructional error was harmless.