delivered the opinion of the court:
In this cause, defendant, Raymond Lee Stewart, who is under sentence of death on two separate murder *109convictions, seeks reversal of the order of the circuit court of Winnebago County that dismissed his second set of post-conviction petitions without an evidentiary hearing. For the following reasons, we affirm.
Defendant’s convictions and sentences were previously affirmed by this court on direct appeal, and the United States Supreme Court denied review. People v. Stewart (1984), 104 Ill. 2d 463 (Stewart I), cert, denied (1985), 471 U.S. 1120, 86 L. Ed. 2d 267, 105 S. Ct. 2368; People v. Stewart (1984), 105 Ill. 2d 22 (Stewart II), cert, denied (1985), 471 U.S. 1131, 86 L. Ed. 2d 283,105 S. Ct. 2666.
Following his direct appeals, defendant filed a petition in each case for relief under the Post-Conviction Hearing Act (Ill. Rev. Stat. 1983, ch. 38, par. 122—1 et seq.). Those first two petitions were consolidated and then dismissed or denied by the circuit court without an evidentiary hearing. While defendant’s appeal from those dismissals was pending, this court ordered a summary remand to determine whether defendant’s counsel had complied with Supreme Court Rule 651(c) (107 Ill. 2d R. 651(c)), which required him, as appointed counsel for an indigent appellant, to show that he had consulted with defendant to ascertain his contentions of deprivation of constitutional right, that he had examined the trial record, and that he had made any necessary amendments to defendant’s pro se petitions. The trial court found that defendant’s counsel had complied with Rule 651(c); this court affirmed that finding and the denial of defendant’s petitions; the United States Supreme Court denied review. People v. Stewart (1988), 121 Ill. 2d 93 (Stewart III), cert. denied (1988), 488 U.S. 900, 102 L. Ed. 2d 234, 109 S. Ct. 246.
*110Defendant then filed his second post-conviction petition in each case, accompanied by voluminous supporting material and by a petition for leave to proceed in forma pauperis and for appointment of counsel, a motion for funds to retain a mitigation expert, a motion for neurological examination, and a motion for psychological examination. The circuit court appointed counsel for defendant, consolidated the petitions, and, on the State’s motion in each case, dismissed each of these second post-conviction petitions without an evidentiary hearing. The circuit court also dismissed defendant’s motions for expert funds and for neurological and psychological examinations.
Defendant then filed his notice of appeal from the circuit court’s dismissal of these second post-conviction petitions. Although defendant and the State look to Supreme Court Rule 603 (107 Ill. 2d R. 603) as jurisdictional authority, we took jurisdiction under Supreme Court Rule 651(a) (107 Ill. 2d R. 651(a)).
In the second petition filed in case No. 81 — CF—194, defendant alleged (1) ineffective assistance of trial counsel; (2) ineffective assistance of counsel on direct appeal, and ineffective assistance of post-conviction counsel during proceedings in both the trial court and appellate court, all for failure to raise claims of ineffective assistance by trial counsel; and (3) denial of equal protection and due process, and denial of the right to be free from cruel and unusual punishment, because the jury was given an instruction later determined by this court (People v. Gacho (1988), 122 Ill. 2d 221) to be incorrect.
In the second petition filed in case No. 81 — CF—196, defendant alleged (1) ineffective assistance of counsel at trial and (2) ineffective assistance of counsel on direct *111appeal, in post-conviction proceedings, and on appeal of those proceedings.
Defendant points out that, in his Stewart III set of post-conviction petitions, no claims of pretrial, trial, or sentencing error or of ineffective assistance of counsel were raised. The Stewart III petitions merely mounted challenges to the constitutionality of the Illinois death penalty. (See Stewart III, 121 Ill. 2d at 96, 104.) We note, however, that on appeal of the dismissal of those petitions, an ineffective-assistance claim was raised regarding alleged noncompliance by post-conviction counsel with Rule 651(c) (see Stewart III, 121 Ill. 2d at 97-103)-a matter to which we have already referred and which led to a hearing on summary remand while the appeal was pending. Also, during later oral argument of the Stewart III appeal, defendant raised for the first time a second ineffective-assistance claim: (1) that during the post-conviction proceedings in the trial court, counsel failed to apprise defendant of a conflict of interest arising from the fact that he had also been defendant’s trial counsel and the alleged fact that he had rendered ineffective assistance at trial and thus could not be expected to raise his own ineffectiveness as a post-conviction claim on defendant’s behalf (see Stewart III, 121 Ill. 2d at 103-04), and (2) that the post-conviction petitions raised only general constitutional claims rather than alleging trial-specific errors (see Stewart III, 121 Ill. 2d at 104).
In deciding Stewart III, we noted that defendant had raised ineffective-assistance claims on the basis of alleged trial error in Stewart I but that they had been decided adversely to him when Stewart I was decided. (Stewart III, 121 Ill. 2d at 104; see Stewart I, 104 Ill. 2d at 491-92, 493-94.) We also noted that, in Stewart II, defendant failed to raise any ineffective-assistance claims regarding the trial proceedings. (Stewart III, 121 Ill. 2d *112at 104-05.) We noted that in the Stewart I and Stewart II direct appeals, defendant was represented by counsel other than the counsel who had allegedly rendered ineffective assistance at trial. (Stewart III, 121 Ill. 2d at 104-05.) We then held that it was not fundamentally unfair to apply doctrines of waiver and res judicata so as to preclude defendant from raising an ineffective-assistance claim during his Stewart III appeal. An additional ground for our decision was that defendant had failed to raise his second ineffective-assistance claim until oral argument, in violation of Supreme Court Rule 341(e)(7) (107 Ill. 2d R. 341(e)(7)). In response to defendant’s assertion that his original post-conviction counsel at the trial court level failed to advise him of a conflict of interest and that his new post-conviction appellate counsel was unaware of that failure until the hearing on remand occurred, we pointed out that, not only was there no evidence that defendant had actually wished to raise an ineffective-assistance claim while being represented by the post-conviction counsel with the alleged conflict, but, more importantly, the alleged errors on which his ineffective-assistance claim was now based had been known to defendant’s counsel on direct appeal, yet no such claim had been raised then. Therefore, defendant was now precluded from raising the claim. Stewart III, 121 Ill. 2d at 105-06.
The ineffective-assistance claims in defendant’s second set of post-conviction petitions, now before us on appeal, traverse more issues than were encompassed by Stewart I, Stewart II, or Stewart III. They also involve additional tiers of allegedly ineffective assistance. Whereas the claims through Stewart III involved allegations of ineffective assistance at trial and in connection with defendant’s first set of post-conviction petitions in the trial court, the present claims also involve allegedly *113ineffective assistance on direct appeal and on appeal of the denial of the first set of petitions.
If enough time for commencing post-conviction proceedings still remained (see Ill. Rev. Stat. 1989, ch. 38, par. 122 — 1), and despite the excellent briefs filed by his present counsel, it is not impossible to imagine defendant’s filing a future, Stewart V post-conviction petition alleging ineffective assistance of counsel in connection with the present Stewart IV appeal. The ineffective-assistance claims in this cause already resemble an intricate puzzle of boxes, each but the largest nestled within one of the others. Still, given the seriousness of capital punishment and the rationale offered by defendant for his present claims, we are obliged to weigh them carefully.
Defendant asserts that the record of the hearing on remand in Stewart III discloses that the absence of trial-specific claims in defendant’s first post-conviction petitions resulted from a transition in counsel while the petitions were being prepared, as follows. Counsel for defendant in one of his two direct appeals testified that she left her position soon after Federal certiorari was denied in connection with those appeals. Before leaving, she drafted a “bare bones” petition addressing only the constitutionality of the death penalty, so that a pleading of some sort would be available for filing while post-conviction counsel investigated defendant’s case. Post-conviction counsel testified that, because he had been defendant’s trial counsel in both trials, he was familiar with the cases; he had reviewed the trial transcripts; and he had had a telephone conversation with defendant in which defendant had stated that he had nothing to add to the allegations in the petitions as drafted by appellate counsel. Defendant refused to testify at this hearing on remand, which was conducted to determine whether *114post-conviction counsel had complied with Rule 651(c). See Stewart III, 121 Ill. 2d at 99-103.
Defendant asserts that the trial-specific allegations in his second set of petitions, if found to be true, would unquestionably warrant relief — at least, new sentencing hearings. The petitions allege:
Improper denial of defendant’s motions to suppress evidence based on alleged defects in search warrant affidavits, issuance, and execution, and resulting ineffective-assistance claims at all levels of his cause for failure to allege such error.
Improper unitary rather than bifurcated sentencing hearings, with resulting ineffective-assistance claims.
Failure of trial counsel to know the law in order to advise the juries that, if defendant were not sentenced to death, he would be sentenced to natural life imprisonment without parole, rather than to present argument on defendant’s rehabilitation potential, with resulting ineffective-assistance claims.
Failure to present, at the sentencing hearings, mitigation evidence of defendant’s prison disciplinary record, with resulting ineffective-assistance claims.
Failure to prepare mitigation witnesses so as to present evidence of defendant’s severely impoverished, deprived, and brutalized upbringing, his expulsion from his household at age 14, and his protection of his mother and siblings from his father’s beatings and expulsions, with resulting ineffective-assistance claims.
Failure to investigate potential mitigation evidence adequately and failure to present available mitigation testimony, with resulting ineffective-assistance claims.
*115Failure to seek psychological or neurological examinations prior to sentencing, with resulting ineffective-assistance claims.
In one of defendant’s cases, systematic prosecutorial exclusion of prospective jurors on the basis of race, with resulting ineffective-assistance claims through failure to pursue this issue at the level of post-trial motion, direct appeal, the first post-conviction petitions and appeal if those petitions would have been denied.
Failure of post-conviction counsel to disclose the alleged conflict of interest already described, with resulting ineffective-assistance claims.
Entitlement of defendant to a new sentencing hearing for failure to advise the juries of the sole natural life imprisonment alternative to the death penalty, as prescribed in People v. Gacho (1988), 122 Ill. 2d 221, and for alleged lack of a rational basis to distinguish defendant’s cases from Gacho, as a result of which defendant claims to have been deprived of due process, equal protection, and the right to be free from cruel and unusual punishment.
Ineffective-assistance claims at all levels of his cause for failure to object at trial to the following alleged errors or to raise them in subsequent proceedings: prosecutorial argument at sentencing that, if not sentenced to death, defendant might be released to kill again; jury instructions not to consider “sympathy” in determining sentence; other rulings on a motion to suppress evidence; and failure to preserve error on denial of a motion to challenge a juror for cause because of his views regarding the death penalty.
And, admission of improper hearsay testimony and admission of prosecution testimony about an un*116disclosed statement of defendant, with resulting ineffective-assistance claims.
Defendant contends that if mitigation evidence of defendant’s upbringing had been investigated and presented, the sentencing juries could reasonably have concluded that the death penalty was not appropriate (cf. Lockett v. Ohio (1978), 438 U.S. 586, 604, 57 L. Ed. 2d 973, 990, 98 S. Ct. 2954, 2964-65), and defendant contends that counsel had a duty to investigate potential sources of mitigation evidence, so that an allegation of unjustifiable failure to investigate should entitle defendant to an evidentiary, hearing (see People v. Ruiz (1989), 132 Ill. 2d 1, 27).
Defendant further contends that failure to introduce evidence of what he terms his relatively good disciplinary record during previous imprisonments not only deprived him directly of possible mitigation evidence in connection with the death penalty but also nullified his right (see Ill. Rev. Stat. 1981, ch. 38, par. 9—1(e); People v. Jones (1982), 94 Ill. 2d 275, 286) to rebut prosecution evidence of defendant’s aggression toward jail officers during pretrial detention in the present cause.
Without elaborating on every contention of his second set of post-conviction petitions, defendant urges that at least some of the contentions set forth constitutional claims adequate to warrant relief if found to be factually true. Defendant therefore contends that the trial court erred in dismissing the petitions on waiver and res judicata grounds.
Defendant contends forcefully that although successive post-conviction proceedings are not normally permissible (People v. Free (1988), 122 Ill. 2d 367, 375-76), they are not necessarily forbidden, and where initial proceedings were fundamentally deficient, successive petitions are appropriate (see Free, 122 Ill. 2d at 376; People *117 v. Nichols (1972), 51 Ill. 2d 244, 246; People v. Hollins (1972), 51 Ill. 2d 68, 70; People v. Slaughter (1968), 39 Ill. 2d 278, 285).
Defendant concludes that proceedings on his first set of post-conviction petitions were fundamentally deficient, that so were proceedings at trial and on direct appeal, and that the record discloses that the alleged deficiencies were not considered and approved by prior counsel but were merely overlooked by them, either inadvertently or because post-conviction counsel would have had to search the record for evidence of his own ineffective assistance. Therefore, defendant argues, when his first post-conviction petitions were filed, he actually had (1) colorable, record-based claims of constitutional error, which could have and would have been presented earlier if he had had effective counsel, and (2) claims of error based on matters dehors the record that could have been presented if his original post-conviction counsel had not labored under a conflict of interest regarding his own ineffectiveness. Thus, defendant seeks reversal of the circuit court’s dismissal order and a remand with directions to conduct evidentiary hearings or enter other appropriate relief.
We determined in Stewart III that it would not be fundamentally unfair to apply waiver and res judicata doctrines so as to preclude defendant from raising ineffective-assistance claims based on alleged trial error. We adhere to that conclusion now, insofar as his present ineffective-assistance claims are based on allegations of trial error.
Of course, many of his present claims are based on various counsel’s performance during direct appeal, presentation of his first post-conviction petitions, and appeal from the denial thereof. Stewart III did not directly decide whether waiver and res judicata principles barred all these latter claims, though Stewart III did decide *118that it was not fundamentally unfair to bar defendant from raising ineffective-assistance claims based on the alleged conflict of interest of his first post-conviction counsel (see Stewart III, 121 Ill. 2d at 103-06) — a conclusion to which we likewise adhere today. Defendant argues that it would be fundamentally unfair to hold him as a lay person responsible for identifying alleged professional derelictions by counsel whose very duty, recognized by existence of the Post-Conviction Hearing Act, was to identify such derelictions. The State, on the other hand, argues that, at least in regard to whatever light defendant might have shed on his present contentions had he not refused to attend the hearing on remand in Stewart III, defendant is chargeable with waiver. Defendant, in turn, denies this contention on two grounds: that he should not be held responsible for judgments of professional dereliction, and that the scope of the hearing on remand could not properly have included the merits of his present claims.
Rather than decide these issues of fairness, we choose to assess defendant’s latest ineffective-assistance claims in light of Strickland v. Washington (1984), 466 U.S. 668, 80 L. Ed. 2d 674, 104 S. Ct. 2052, and People v. Caballero (1989), 126 Ill. 2d 248.
Under Strickland, in order to establish a claim of ineffective assistance of counsel, a defendant generally must show (1) that despite a strong presumption of counsel’s professional competence, counsel’s allegedly unprofessional acts or omissions in fact were “outside the wide range of professionally competent assistance,” and (2) that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” (Strickland, 466 U.S. at 690, 694, 80 L. Ed. 2d at 695, 698, 104 S. Ct. at 2066, 2068.) To establish a “reasonable probability,” it is not enough to show that the alleged errors “had some *119conceivable effect on the outcome.” On the other hand, a defendant “need not show that counsel’s deficient conduct more likely than not altered the outcome.” Rather, a “reasonable probability” is simply “a probability sufficient to undermine confidence in the outcome.” (Strickland, 466 U.S. at 693-94, 80 L. Ed. 2d at 697-98, 104 S. Ct. at 2067-68.) If it is easier to decide an ineffective-assistance claim on the ground of lack of sufficient prejudice rather than on the issue of whether counsel’s performance was constitutionally deficient, a court should do so .Strickland, 466 U.S. at 697, 80 L. Ed. 2d at 699, 104 S. Ct. at 2069.
A defendant who maintains that appellate counsel rendered ineffective assistance, for example by failure to argue a particular issue, must show that “the failure to raise that issue was objectively unreasonable” and that, “but for this failure, his sentence or conviction would have been reversed.” Caballero, 126 Ill. 2d at 270.
Here, defendant argues that if the allegations in his second post-conviction petitions were now found on evidentiary hearing to be true, they would warrant substantial relief, including at least a new sentencing hearing. However, the real issue is whether earlier counsel on direct appeal and in connection with defendant’s first post-conviction petitions rendered ineffective assistance by failing to raise such of these allegations as we have not already held to be barred for ineffective-assistance claim purposes. The resolution of that issue turns on whether, absent such failure, defendant’s sentences or convictions would have been reversed.
We have already held that defendant’s ineffective-assistance claims with regard to matters of record at his trial are barred. Thus, as far as trial proceedings are concerned, we are left with his ineffective-assistance claims regarding matters outside the record — namely, failure to investigate and present mitigation evidence of *120defendant’s prison disciplinary record and childhood experiences, and failure to seek psychological or neurological examinations.
We do not believe that, but for failure of counsel on direct or in post-conviction proceedings to raise these latter claims, defendant’s convictions or sentences would have been reversed, or even that a reasonable probability exists that reversal would have been ordered. Our reason for so concluding is that defendant has not shown that, but for the alleged omissions of trial counsel on which these appellate and post-conviction ineffective-assistance" claims are based, there is a reasonable probability that defendant’s juries would have returned different verdicts and findings.
Defendant does argue that if the alleged omissions had not occurred and the evidence at issue had been presented to a jury, the jury “could reasonably have concluded” that the death penalty was inappropriate — in other words, that the evidence not submitted “could have resulted in a sentence other than death.” However, the Strickland ineffective-assistance test is not whether the jury reasonably could have decided otherwise; the test is whether defendant has shown a reasonable probability, not merely a conceivable possibility, that the jury would have reached a different decision. This he does not even claim to have shown. Moreover, we do not believe that such a reasonable probability exists. The aggravation evidence at defendant’s sentencing hearings was so overwhelming that there is no reasonable probability of a different jury decision if the hypothesized mitigation evidence had been presented — particularly in view of the fact that defense counsel did present many witnesses who testified to defendant’s character, childhood, and rehabilitation potential. And, even if a reasonable probability did exist that, with the additional evidence, a jury would have decided differently, defendant has not *121established that failure to present the additional evidence met Strickland’s professional-incompetence requirement rather than presumably having been trial strategy.
The final point raised by defendant’s second set of post-conviction petitions is his alleged entitlement to a new sentencing hearing on the ground that there is no rational basis to distinguish the jury instructions in his cases from the instruction ruled incorrect in People v. Gacho (1988), 122 Ill. 2d 221. The circuit court’s dismissal order rejected this point, as the following portion of the transcript demonstrates:
“With regard to the defendant’s entitled now to a new sentencing hearing based on the decision in the Gacho case, I certainly read that opinion as quite clearly indicating to this Court that it doesn’t apply to these cases. If counsel argues that there is some underlying constitutional right to be protected, I would say that that was certainly not ignored by the court when it made its decision in Gacho. I don’t pretend to understand the exquisite reasoning that led them to that decision, but whatever the decision is, I think — I believe it does not require that this Court consider that this should be any exception to the stated rule that they’ve promulgated.”
In Gacho, this court directed trial courts to use the correct instruction on the natural life imprisonment alternative to the death penalty in all sentencing hearings conducted after February 11, 1988. (Gacho, 122 Ill. 2d at 262-63.) Before Gacho, the established case law in Illinois was that it was not error to fail to give such an instruction. (See Gacho, 122 Ill. 2d at 260, 262.) Defendant’s sentencing hearings were conducted before the decision in Gacho was announced.
Defendant’s brief on appeal does not address this point. Accordingly, under Supreme Court Rule 341(e)(7) (107 Ill. 2d R. 341(e)(7)) it is waived.
*122For the reasons stated herein,- the trial court’s dismissal of defendant’s second post-conviction petitions is affirmed. The clerk of this court is directed to enter an order fixing Tuesday, March 12, 1991, as the date on which the sentences of death entered in the circuit court are to be executed. Execution of defendant’s sentences shall be by lethal injection in the manner provided by section 119 — 5 of the Code of Criminal Procedure of 1963 (Ill. Rev. Stat. 1989, ch. 38, par. 119 — 5). A certified copy of this order shall be furnished to the Director of Corrections, to the warden of Stateville Correctional Center, and to the warden of the institution .wherein defendant is confined.
Judgment affirmed..