SILER, J., delivered the opinion of the court, in which COLE, J., joined. MERRITT, J. (pp. 1013-17), delivered a separate dissenting opinion.
AMENDED OPINION
SILER, Circuit Judge.Twenty years ago, Archie Dixon and his accomplice brutally attacked Christopher Hammer and buried him alive. Dixon was convicted of aggravated murder, robbery, kidnaping, and forgery, and the state trial court sentenced him to death. He sought to vacate his conviction and sentence, asserting that his confession was obtained in violation of his Miranda rights and alleging numerous errors in his trial. We ruled that his confession was coerced, deeming his remaining claims regarding effectiveness of trial counsel, the instructions to the jury, and the exclusion of certain mitigating evidence pretermitted. On review, the Supreme Court reversed our ruling, see Bobby v. Dixon, — U.S.-, 132 S.Ct. 26, 181 L.Ed.2d 328 (2011), and we must now review his remaining claims for ineffective assistance of counsel, improper jury instruction, and the exclusion of certain mitigating evidence at his penalty hearing. For the following reasons, we AFFIRM the district court’s ruling and DENY Dixon’s petition for a writ of habeas corpus.
I.
Dixon and his accomplice, Timothy Hoff-ner, were friends with Hammer. In 1993, Dixon and Hoffner beat Hammer, tied him to a bed, stole the contents of his wallet and his automobile, and then drove him into a remote area and buried him alive. One month into the ensuing investigation, Hoffner led police to Hammer’s body and Dixon provided a tape-recorded account of the kidnaping, robbery, and murder.
Dixon was indicted for aggravated murder, kidnaping, and aggravated robbery. At trial, the defense presented no evidence and cross-examined only three of the prosecution’s 15 witnesses. The jury convicted Dixon on all charges and recommended *1007the death penalty, which the court imposed. Dixon appealed his conviction to the Ohio Court of Appeals and, while that appeal was pending, he filed a post-conviction petition with the trial court, arguing ineffective assistance of counsel. The latter was denied, and Dixon appealed that decision to the Ohio Court of Appeals. The Ohio Court of Appeals consolidated Dixon’s direct appeal and post-conviction appeal and affirmed his conviction. He then appealed to the Ohio Supreme Court, which also affirmed, State v. Dixon, 101 Ohio St.3d 328, 805 N.E.2d 1042, 1063 (2004).
Dixon proceeded to file a federal habeas petition alleging ineffective assistance of counsel, improper jury instructions, improper exclusion of mitigating evidence at sentencing, and a violation of his Miranda rights.1 The district court denied the petition, and Dixon appeals.
II.
Under 28 U.S.C. § 2254(d), as amended by the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”), a habeas corpus application which includes a claim that was previously adjudicated on the merits in state court proceedings will be “denied unless the state court decision was contrary to, or involved an unreasonable application of, clearly established federal law as determined by the Supreme Court, or based on an unreasonable determination of the facts in light of the evidence presented to the state courts.” Cullen v. Pinholster, — - U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011). This standard is “difficult to meet,” “highly deferential,” and “demands that state-court decisions be given the benefit of the doubt.” Id. (quoting Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (per curiam)). Dixon carries the burden of meeting this high bar.
The parties initially dispute whether Dixon’s claims were adjudicated on the merits and, accordingly, whether AED-PA’s standard of review applies and whether our review is limited to the record before the state court. “By its terms § 2254(d) bars relitigation of any claim ‘adjudicated on the merits’ in state court, subject only to the exception in §§ 2254(d)(1) and (d)(2).” Although the Supreme Court has not defined “adjudication on the merits,” we are guided by its observation that “no text in the statute requires] a statement of reasons.” Harrington v. Richter, — U.S.-, 131 S.Ct. 770, 784, 178 L.Ed.2d 624 (2011). Rather, the “statute refers only to a ‘decision,’ which resulted from an ‘adjudication.’ ” Id. Thus, “[w]hen a federal claim has been presented to a state court and the state court has denied relief, it may be presumed that the state court adjudicated the claim on the merits in the absence of any indication or state-law procedural principles to the contrary.” Id. at 784-85.
Each of Dixon’s claims on appeal was adjudicated on the merits in state court. First, he argued that defense counsel was ineffective by cross-examining only three of the state’s 15 witnesses at trial. The Supreme Court of Ohio found that “[c]oun-sel’s tactical decisions reflected reasonable representation.” Dixon, 805 N.E.2d at 1054. Second, Dixon argued he was denied the effective assistance of counsel during his mitigation hearing because counsel failed to present available mitigating evidence. The Supreme Court of Ohio *1008found that, based upon the evidence before the trial court, it was impossible to determine that sufficient mitigating evidence existed to “eall[] for a sentence less than death.” Id. at 1056. Third, Dixon argued that the trial court erred in excluding certain evidence at mitigation. Specifically, Dixon had previously been wrongfully incarcerated on a rape charge that was subsequently dismissed. The Supreme Court of Ohio found that although the trial court should have permitted the evidence, excluding it was harmless error. Id. Fourth, Dixon argued that the trial court erred in its penalty-phase instructions regarding aggravating circumstances in Dixon’s actions. The Supreme Court of Ohio adjudicated this argument in detail and found the instructional error did not constitute grounds for reversal. Id. at 1059. Finally, Dixon argued that the trial court erroneously instructed the jury to assume his guilt. Here, as well, the Supreme Court of Ohio found no plain error, concluding that “the jury was properly charged on the presumption of innocence, reasonable doubt, and the burden of proof.” Id. at 1053. Because all of Dixon’s arguments on appeal were adjudicated on their merits by the Supreme Court of Ohio, our highly-deferential review under AEDPA is limited to the record before that court.
A.
In order to prevail on a claim of ineffective assistance of counsel, Dixon “must show both that his counsel’s performance was deficient and that the deficient performance prejudiced the defense.” Hodges v. Colson, 711 F.3d 589, 613 (6th Cir.2013) (citing Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984)). To show deficiency, Dixon must establish that “counsel made errors so serious that [he] was not functioning as the ‘counsel’ guaranteed ... by the Sixth Amendment.” Strickland, 466 U.S. at 687, 104 S.Ct. 2052. To show prejudice, Dixon must establish that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. 2052. We need not address both components if we find that Dixon has failed to meet one of them. Id. at 697, 104 S.Ct. 2052.
Dixon first argues that his due process right to a fair trial was prejudiced by defense counsel’s failure to cross-examine several of the prosecution’s witnesses. Moreover, Dixon argues that the cross-examination which was conducted was insufficient and ineffective. Defense counsel cross-examined three witnesses at trial: Jennifer Wodarsky, Hammer’s former girlfriend; Barbara Hammer, Hammer’s mother; and Detective Phil Kulakoski, who questioned Dixon at the Toledo Police Department two weeks after the murder. Counsel challenged the state’s portrayal of Hammer as an innocent young man by asking Wodarksi and Barbara Hammer about Hammer’s involvement with drugs and misuse of a credit card, and questioned Kulakoski about the discovery of Hammer’s body near the Michigan state border, a state without the death penalty, in an attempt to suggest the arbitrariness of Ohio’s death penalty. The Supreme Court of Ohio found that “[cjounsel’s tactical decisions reflected reasonable representation,” and noted that courts “must indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Dixon, 805 N.E.2d at 1054 (quoting Strickland, 466 U.S. at 689, 104 S.Ct. 2052). Furthermore, the court found that counsel’s decision not to cross-examine other witnesses resulted from his realization “that any attempt to cross-examine [them] would have merely reemphasized their damaging testimony.” Id. at 1055.
*1009On appeal, Dixon argues that his counsel’s brief and his decision to otherwise not cross-examine or call additional witnesses amounted to “defense counsel put[ting] their hands up and surrender[ing].” And, although Dixon admits that cross-examination techniques, like other matters of trial strategy, are entrusted to the professional discretion of cotmsel, he questions how any strategy can be “based upon asking absolutely no questions.” He specifically argues that counsel should have cross-examined Kirsten Wilkerson, Dixon’s girlfriend, who offered a first-hand account of the murder, since she was present during Hammer’s beating. Dixon argues that Wilkerson provided inconsistent accounts of the incident during multiple statements to police, which counsel should have investigated. Furthermore, he argues that counsel should have performed a more thorough cross-examination of Kulakoski about the conditions under which Dixon’s confession was obtained.
Despite any shortcomings in counsel’s performance or the quality of his strategy, Dixon must show that the performance was unreasonable and that it prejudiced the case in order to succeed on his claim. That he cannot do. Beyond questioning Wodarski and Barbara Hammer about the victim’s drug use and financial indiscretions, any further badgering by defense counsel could have easily offended a rational juror and backfired on the defense. Moreover, prodding Wilkerson on cross-examination about the inconsistencies in her testimony would bring to light Dixon’s taped confession to the murder and, quite possibly, the history of domestic violence in Dixon and Wilkerson’s relationship, which might explain her fear in testifying against Dixon truthfully. As the Ohio Court of Appeals recognized in Dixon’s first appeal, “the overwhelmingly incriminating nature of the evidence against appellant as well as the certainty with which each witness offered his or her testimony” made cross-examination imprudent as it would have only further emphasized the credible, incriminating evidence against him. State v. Dixon, no. L-96-004, 2000 WL 1713794, at *5 (Ohio App.6 Dist. Nov. 17, 2000). The Supreme Court of Ohio agreed with this reasoning, finding that even if counsel’s performance was unreasonable, Dixon could not show that it prejudiced his case.
' We agree that Dixon cannot show prejudice in light of the amount and quality of incriminating evidence presented against him at trial. Dixon must demonstrate that “counsel’s errors were so serious as to deprive [him] of a fair trial, a trial whose result is reliable.” Strickland, 466 U.S. at 688, 104 S.Ct. 2052. He “must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the "proceeding would have been different.” Id. at 694,104 S.Ct. 2052. The overwhelming evidence presented against Dixon revealed that Dixon brutally attacked Hammer, buried him alive, and then attempted to steal Hammer’s identification (by making a false identification card containing his photo and Hammer’s personal information), obtained new title to Hammer’s car, and sold the vehicle -for $2,800. Cross-examining Wilkerson and Kulakoski in more detail, or questioning other witnesses for that matter, would have had virtually no effect on Dixon’s convictions in light of the evidence that was presented. The state courts’ denial of Dixon’s ineffective-assistance-of-counsel claim neither contradicted nor unreasonably applied Supreme Court precedent as required by 28 U.S.C. § 2254(d).
B.
Dixon argues that the district court erroneously instructed the jury on the *1010proper burden of proof required to sustain his conviction. The jury was charged:
Thus, assuming a finding of the defendant is guilty beyond a reasonable doubt of the aggravated murder with prior calculation and design of Christopher Hammer as charged in Count 1 of the indictment, and further assuming a finding as to Specification 1 that the aggravated murder of Christopher Hammer was committed during the course of a kidnapping, and further finding beyond a reasonable doubt that the defendant, Archie J. Dixon, was either a principal offender in that murder or that the aggravated murder was committed with prior calculation and design, will mandate a finding of guilty as to Specification 1.
Dixon argues that the “assumption of guilt” deprived him of his due process right to a fair trial because it required the jury to infer a certain fact if the state proved specific predicate facts, relieving the state from proving every element of the offense.
Dixon’s argument fails for two reasons. First, Dixon disingenuously isolates one portion of the jury instructions and asks us to interpret them without reference to additional instructions provided to the jury. Prior to reading the instructions above, the trial court first described each step of the deliberation process, carefully explaining the requirement that jurors be convinced beyond a reasonable doubt in order to return a guilty verdict. The instructions cited by Dixon came after the court discussed the first aggravated murder count and the first capital specification. Only then did the court instruct jurors that if they found Dixon guilty of (1) aggravated murder with prior calculation and design; (2) which was committed during the course of a kidnaping; and (3) in which he was a principal offender, then they should return a guilty verdict as to Specification 1. Thus, at no time did the district court erroneously mandate that the jury assume Dixon’s guilt.
Even if the court’s instruction could be understood as an assumption of guilt, we review jury instructions “as a whole, in order to determine whether they adequately informed the jury of the relevant considerations and provided a basis in law for aiding the jury in reaching its decision.” United States v. Frederick, 406 F.3d 754, 761 (6th Cir.2005). Here, the trial court meticulously and repeatedly instructed the jury as to the proper burden of proof. (“The defendant is presumed innocent until his guilt is established beyond a reasonable doubt. The defendant must be acquitted unless the State produced evidence which convinces you beyond a reasonable doubt of every essential element of the offense charged in the indictment.”). We grant habeas relief where an “ailing instruction by itself so infected the entire trial that the resulting conviction violates due process,” Cupp v. Naughten, 414 U.S. 141, 147, 94 S.Ct. 396, 38 L.Ed.2d 368 (1973), and such is clearly not the case here.
C.
Dixon argues that the trial court wrongfully excluded mitigating evidence at his penalty hearing. Prior to the hearing, his counsel informed the court that he intended to introduce evidence of the following: (1) two unrelated capital murder cases in Lucas County where the state had not sought the death penalty in exchange for defendants’ guilty pleas to aggravated murder charges; (2) Dixon’s acceptance of responsibility for his crimes as evidenced by his offering to plead guilty to the charges in exchange for dismissal of the death penalty specifications; and (3) Dixon’s prior, unrelated incarceration on a *1011rape charge, which, was based on false allegations and was subsequently dismissed. The trial court excluded each of these, and Dixon now argues that their exclusion violates his due process rights.
In Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), Supreme Court held:
the Eighth and Fourteenth Amendments require that [a] sentencer, in all but the rarest kind of capital case, not be precluded from considering, as a mitigating factor, any aspect of a defendant’s character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death.
Despite the inclusive language of this rule, the Supreme Court consistently illustrates that mitigating evidence offered by a defendant must still fall within the spectrum of relevance in order to be admissible. Eddings v. Oklahoma, 455 U.S. 104, 115, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982) (the sentencer may not “refuse to consider ... any relevant mitigating evidence.”). In fact, the Supreme Court in Lockett expressly reserved this limitation, noting that “nothing in [its] opinion limits the traditional authority of a court to exclude, as irrelevant, evidence not bearing on the defendant’s character, prior record, or the circumstances of his offense.” Lockett, 438 U.S. at 605 n. 12, 98 S.Ct. 2954. Thus, we must ask whether the evidence presented by Dixon was relevant, and therefore automatically admissible, as he insists.
The Ohio Supreme Court determined that the trial court’s decision to exclude the information was erroneous because “it fits within the ‘history, character, and background of the offender.’ ” Dixon, 805 N.E.2d at 1057 (citing State v. Stumpf, 32 Ohio St.3d 95, 512 N.E.2d 598, 605 (1987)). Nevertheless, it considered the error to be harmless as “our independent reassessment of the sentence will minimize any prejudicial impact.” Id. (citations omitted). In its independent sentence evaluation, it went on to “conclude that this factor has little, if any relevance to whether Dixon should be sentenced to death.” Id. at 1062. Because the Ohio Supreme Court reviewed this claim as a matter of state law only, rather than as an Eighth Amendment claim, the district court conducted de novo review. It agreed that the trial court’s decision constituted harmless error, explaining that “given the overwhelming aggravating evidence, and the lack of mitigating evidence, the exclusion of the false imprisonment does not undermine the Court’s confidence in the outcome of the sentencing phase of trial.”
Dixon asserts that this alleged error is not subject to harmless error review, because it is a structural error. However, the error here was not structural as the issue involves the trial court’s decision to exclude certain mitigating evidence and is therefore subject to harmless error review. See Hitchcock v. Dugger, 481 U.S. 393, 399, 107 S.Ct. 1821, 95 L.Ed.2d 347 (1987) (exclusion of mitigating evidence renders death sentence invalid in the absence of a showing of harmless error). Given the specific facts . of Dixon’s crime and the compelling aggravating evidence in this case, evidence of Dixon’s prior wrongful incarceration due to unrelated rape allegations would, at best, have been negligibly mitigating. We do not believe that its exclusion had any substantial effect on Dixon’s sentencing. See Brecht v. Abrahamson, 507 U.S. 619, 639, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). The Ohio Supreme Court’s conclusion that the exclusion of Dixon’s, wrongful incarceration was harmless is therefore not contrary to clearly established federal law.
D.
Dixon next claims that his counsel was ineffective for failing to present *1012mitigating evidence at the penalty phase of trial. He focuses almost entirely on two investigations prepared for the mitigation phase of trial. Following Dixon’s conviction, defense counsel hired Dr. Christopher Layne, a board-certified clinical psychologist, to examine Dixon for neurological impairments and review his medical records. In his oral report supplied to defense counsel, Layne found no evidence of brain damage and diagnosed Dixon with “antisocial personality disorder” and a criminal personality. Counsel also hired Gary Ericson, a defense mitigation specialist, to research Dixon’s social history. After interviewing Dixon’s mother, brother, foster parents, family pastor, and parole officer, Ericson submitted a written report to counsel showing that Dixon’s family history included domestic violence, sexual abuse, physical aggression, possible incest, and alcoholism. Although both of these investigations were available to counsel before sentencing, they were not used as evidence in mitigation.
The state courts adjudicated Dixon’s ineffective-assistance-of-eounsel claim on the merits and considered Ericson’s report but considered no evidence of the oral report from Layne. In the federal district court below, an evidentiary hearing was held, which revealed Layne’s opinion, but our review is limited by AEDPA to the record before the state courts.2 Pinholster, 131 S.Ct. at 1398. “In assessing whether a defendant’s counsel was ineffective at the mitigation hearing for failing to introduce certain evidence, the focus must be on whether the investigation supporting counsel’s decision ... was itself reasonable.” Clark v. Mitchell, 425 F.3d 270, 284 (6th Cir.2005). This rule takes root in the longstanding and sound principle that matters of trial strategy are left to counsel’s discretion. Thus, where a defendant focuses on counsel’s “strategic choices made after thorough investigation of law and facts,” the Supreme Court guides us that such choices “are virtually unchallengeable.” Strickland, 466 U.S. at 690, 104 S.Ct. 2052 (emphasis added).
In the state trial court, Dixon challenged his counsel’s performance at the mitigation stage, but offered minimal support for his claim. He presented no evidence of what his mitigation witnesses might have testified to and offered minimally helpful affidavits in support thereof. He submitted an affidavit from his mother which vaguely referenced problems he had with his father and another sparse affidavit from his brother that described their family environment as disruptive and dysfunctional. Neither affiant detailed violence, abuse, emotional hardships, or substance abuse from Dixon’s childhood. Dixon’s counsel nevertheless did attempt to offer mitigating evidence, as we discussed above, which the trial court excluded. For this reason, counsel’s performance at the mitigating hearing cannot be considered unreasonable.
E.
Dixon finally argues that the district court erred in its instructions to the *1013jury regarding aggravating circumstances. In its penalty-phase instructions, the trial court identified three aggravating circumstances for the- jury’s consideration: “(1) That the defendant ... caused the death of Christopher Hammer with prior calculation and design and was the principal offender in the aggravated riiurder; (2) That the defendant ... caused the death of Christopher A. Hammer while the defendant was committing kidnapping and that the defendant was the principal offender; and (3) That the defendant ... caused the death of Christopher A. Hammer while the defendant was committing aggravated robbery, and the defendant was the principal offender.” Under Ohio Revised Code § 2929.04(A), “prior calculation and design” is a relevant factor “only if the defendant is not a principal offender.” Thus, the instruction erroneously presented the first factor in conjunction with the second and third factors. The Supreme Court of Ohio recognized this fault and proceeded to “cure” the error by performing an independent reassessment of the sentencing.
A state appellate court may uphold a death sentence that is based in part on invalid instructions regarding aggravating circumstances by reweighing the aggravating and mitigating factors. Clemons, 494 U.S. at 748, 110 S.Ct. 1441. Dixon agrees that this is permissible, but he challenges whether the Supreme Court of Ohio adequately reweighed the factors on review. We conclude that it did. After identifying the instructional error, the Supreme Court of Ohio reviewed relevant precedent and concluded that the error “did not irrevocably taint the jury’s deliberative process.” Dixon, 805 N.E.2d at 1059. It observed that there was a “dearth of mitigating evidence in this case.... During the sentencing phase, the only evidence offered in mitigation was Dixon’s age at the time of the offense and testimony computing the amount of jail time Dixon would serve if given a life sentence.” Id. (citations omitted). “In contrast,” it noted that “the evidence ... overwhelmingly proved the aggravating circumstances,” and that the jury convicted Dixon of aggravated murder. Id. It is evident that the Supreme Court of Ohio thoroughly and thoughtfully reviewed the instructional error, and it therefore comported with Clemons and cured any error that may have occurred.
The district court’s ruling is AFFIRMED and Dixon’s petition for a writ of habeas corpus is DENIED.
. The Miranda issue has been adjudicated, leaving only the first three claims to be addressed. See Dixon v. Houk, 627 F.3d 553 (6th Cir.2010), rev’d.,-U.S.-, 132 S.Ct. 26, 181 L.Ed.2d328 (2011).
. Dixon attempts to circumvent the proper standard of review in this case by relying on Martinez v. Ryan, - U.S. -, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012), and Trevino v. Thaler, - U.S. -, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). These cases stand for the proposition that the failure of counsel to properly litigate post-conviction ineffective-assistance-of-counsel claims in state court may excuse a defendant's procedural default and allow him to file a petition for a writ of habeas corpus in federal court. These cases do not assist Dixon since he alleges no procedural error and in fact presented his ineffective-assistance-of-counsel claim below.