OPINION
Justice NIGRO.Appellant Seifullah Abdul-Salaam appeals from the order of the Court of Common Pleas of Cumberland County denying his petition for relief under the Post Conviction Relief Act (PCRA), 42 Pa.C.S. § 9541 et seq. For the reasons outlined below, we affirm.
On March 15, 1995, a jury found Appellant guilty of first-degree murder, robbery and conspiracy in connection with the fatal shooting of Officer Willis Cole of the New Cumberland Police Department. Following a sentencing hearing, the jury determined that the four aggravating circumstances it found outweighed the one mitigating circumstance it found and accordingly, fixed Appellant’s penalty at death.1 On June 18, 1996, this Court affirmed Appellant’s judgment of sentence. Commonwealth v. Abdul-Salaam, 544 Pa. 514, 678 A.2d 342 *83(1996). Appellant then filed a pro se PCRA petition on May 13, 1997. The Center for Legal Education, Advocacy and Defense Assistance (CLEADA) was appointed to represent Appellant and subsequently filed an amended PCRA petition on Appellant’s behalf. Following a hearing, the PCRA court denied relief. Appellant then filed the instant appeal.2
Appellant raises ten issues in his brief to this Court, many of which contain several sub-issues. Most of Appellant’s issues, however, have been waived for purposes of the PCRA.
To be eligible for relief under the PCRA, a petitioner must establish, as a threshold matter, that his allegations have not been waived. An allegation is deemed waived “if the petitioner could have raised it but failed to do so before trial, at trial, during unitary review [or] on appeal....” 42 Pa.C.S. § 9544(b). In addition, the relaxed waiver rule is not applicable to PCRA capital appeals. See Commonwealth v. Albrecht, 554 Pa. 31, 720 A.2d 693, 700 (1998).
Appellant specifically contends that: the Commonwealth withheld exculpatory evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963); the Commonwealth violated his due process rights by consuming an entire blood sample for testing; the trial court erred by failing to provide instructions to the jury that it could consider evidence of Appellant’s abusive background under 42 Pa.C.S. § 9711(e)(2) and (e)(3), which embody Pennsylvania’s two mental health mitigating circumstances; the process by which this Court engages in proportionality review violates defendants’, including Appellant’s, due process rights; the trial court erred by allowing Appellant’s juvenile adjudications to serve as a basis for the aggravating circumstance under 42 Pa.C.S. § 9711(d)(9), i.e. that the defendant has a significant history of felony convictions involving the use or threat of violence; the aggravating circumstance under 42 Pa.C.S. *84§ 9711(d)(9) is unconstitutionally vague; and the jury improperly found the existence of the aggravating circumstance under 42 Pa.C.S. § 9711(d)(6). Appellant could have raised . each of these claims in his direct appeal to this Court but failed to do so. Accordingly, these claims are waived and, therefore, beyond the power of this Court to review under the express terms of the PCRA. See 42 Pa.C.S. § 9543(a)(3).3
Appellant also argues that trial counsel rendered ineffective assistance of counsel at his penalty phase hearing. Because this claim is framed as one of ineffectiveness, and because it is adequately argued under the standard governing such a claim, this claim has not been waived for purposes of the PCRA and is therefore, reviewable.
To prevail on a claim alleging counsel’s ineffectiveness under the PCRA, Appellant must demonstrate (1) that the underlying claim is of arguable merit; (2) that counsel’s course of conduct was without any reasonable basis designed to effectuate his client’s interest; and (3) that he was prejudiced by counsel’s ineffectiveness, i.e. there is a reasonable probability that but for the act or omission in question the outcome of the proceeding would have been different. Commonwealth v. Kimball, 555 Pa. 299, 724 A.2d 326, 333 (1999); Commonwealth v. Douglas, 537 Pa. 588, 645 A.2d 226, 230 (1994). If a reasonable basis exists for the particular course chosen by counsel, the inquiry ends and counsel’s performance is deemed constitutionally effective. Commonwealth v. Derk, 553 Pa. 325, 719 A.2d 262, 266 (1998) (opinion in support of affirmance).
*85Appellant claims that counsel was ineffective for failing to locate evidence of his mental illness and his organic brain damage and present such evidence as mitigation at his penalty phase hearing. Even if this claim had arguable merit,4 we agree with the PCRA court that counsel had a reasonable basis for not presenting such evidence. At the PCRA hearing, counsel specifically stated his reasons for not presenting mental health mitigation evidence in this particular case, testifying that:
When you begin to defend a person’s actions or excuse them by the use of mental health expert testimony, you hold yourself open to the risk that you are essentially relitigating the crime. I heard this today during your cross-examination of Dr. Armstrong [one of the mental health experts presented by Appellant]. You asked her if she could tell that there was a specific time on August 19th, 1994 [the date Appellant shot and killed Officer Cole], when the organic brain disorder manifested itself in compelling the defendant’s actions, and she said she could not and no one could. The risk of that is that it often provides the prosecutor with an opportunity to not just describe the defendant’s acts in a factual context, but in almost a moral context. For example if a person — taking this case as an example, if a person was afflicted by organic brain disorder or some psychiatric disease or some mental health problem, I’ve heard asked repeatedly in other cases, isn’t this inconsistent with the type of planning that goes into the perpetration of this crime? Isn’t this inconsistent with the fact that the person, according to the evidence and testimony, had the wherewithal to try to escape? *86Isn’t this inconsistent with the fact that he returned to the scene of the crime for perhaps no other reason than to open fire? In a case like this, in this case in particular, the emotional impact of the testimony throughout the trial was such that I would have thought it unlikely that a jury would accept psychiatric mitigation as a factor, especially one that would outweigh the really very devastating emotional impact of the several days of testimony that they just heard.
N.T., 4/23/98, at 179-80. See also Commonwealth v. Pirela, 556 Pa. 32, 726 A.2d 1026, 1035 (1999) (presentation of evidence of defendant’s troubled childhood might be viewed as attempt to trivialize brutal murder). This testimony sufficiently supports the PCRA court’s finding that counsel had a reasonable basis for not presenting the mitigating evidence Appellant now claims counsel should have offered.5
In sum, all but one of Appellant’s claims have been waived and thus, cannot be reviewed by this Court. Appellant’s remaining claim is without merit, as we find that the PCRA court properly determined that counsel did not render ineffective assistance at Appellant’s penalty phase hearing. The order of the PCRA court denying post-conviction relief is therefore affirmed.6
Justices CASTILLE and SAYLOR file concurring opinions.. The jury found the following aggravating circumstances: 1) the victim was a peace officer killed in the performance of his duties, 42 Pa.C.S. § 9711(d)(1); 2) Appellant committed the killing while in the perpetration of a felony, 42 Pa.C.S. § 9711(d)(6); 3) in the commission of the offense, Appellant knowingly created a grave risk of death to another person in addition to the victim, 42 Pa.C.S. § 9711(d)(7); and 4) Appellant has a significant history of felony convictions involving the use or threat of violence, 42 Pa.C.S. § 9711(d)(9). The mitigating circumstance found by the jury was "[a] background that includes both physical and mental abuse does have a negative impact on a person’s development and therefore his future behavior,” pursuant to 42 Pa.C.S. § 9711(e)(8).
. When reviewing the denial of post-conviction relief, this Court is limited to "examining whether the lower court's determination is supported by the evidence of record and whether it is free of legal error.” Commonwealth v. Morales, 549 Pa. 400, 701 A.2d 516, 520 (1997).
. A petitioner can avoid a finding of waiver under the PCRA by making an adequate and properly layered claim of ineffective assistance of counsel at his first available opportunity to do so. Commonwealth v. Wallace, 555 Pa. 397, 724 A.2d 916, 921 (1999). Appellant, in his final issue, makes a bald one-sentence allegation that trial counsel was ineffective for failing to litigate the claims raised on this appeal. Such an undeveloped argument, which fails to meaningfully discuss and apply the standard governing the review of ineffectiveness claims, simply does not satisfy Appellant's burden of establishing that he is entitled to any relief.
. Based on an independent review of the record, we note that we find no error in the PCRA court’s conclusion that the testimony at the PCRA hearing failed to establish that Appellant suffers from organic brain damage or any other mental illness. See PCRA Ct. Op., 11/12/98, at 11, 13. As the Commonwealth observes in its brief, the defense mental health experts could not testify as to when Appellant contracted organic brain damage, how he contracted it, or what effect, if any, it had on him on the day he murdered Officer Cole. Moreover, there was testimony from Dr. Lawrence Rotenberg, who also examined Appellant, that Appellant does not, in his opinion, have organic brain damage. See N.T., 5/1/98, at 136.
. Appellant also claims that trial counsel was ineffective for failing to present evidence of the abuse he suffered as a child. This claim is specious in light of the fact that even Appellant concedes that counsel presented the testimony of several family members who described Appellant's abusive upbringing. If Appellant is suggesting that counsel should have called additional family members to reiterate that Appellant had been abused as a child, this claim also fails as such testimony would have merely been cumulative. See Commonwealth v. Whitney, 550 Pa. 618, 708 A.2d 471, 477 (1998) (counsel not ineffective for failing to call witness at penalty phase who would merely have given cumulative mitigating evidence). In addition, we note that the jury specifically found Appellant's abusive background to be a mitigating circumstance.
. The Prothonotary of the Supreme Court is directed to transmit the complete record of this case to the Governor of Pennsylvania. See 42 Pa.C.S. § 971 l(i).