
738 N.E.2d 500 (2000)
193 Ill.2d 256
250 Ill.Dec. 284
The PEOPLE of the State of Illinois, Appellee,
v.
Robert L. FAIR, Appellant.
No. 84731.
Supreme Court of Illinois.
September 28, 2000.
*501 Frederick F. Cohn, of Chicago, for appellant.
James E. Ryan, Attorney General, of Springfield, and Richard A. Devine, State's Attorney, of Chicago (William L. Browers, Assistant Attorney General, of Chicago, and Renee Goldfarb, Linda D. Woloshin and James E. Fitzgerald, Assistant State's Attorneys, of counsel), for the People.
Justice HEIPLE delivered the opinion of the court:
The petitioner, Robert Fair, appeals from a Cook County circuit court order dismissing his post-conviction petition without an evidentiary hearing. Because petitioner was sentenced to death, this court has jurisdiction over the instant appeal pursuant to Supreme Court Rule 651(a) (134 Ill.2d R. 651(a)). For the following reasons, we now affirm in part and reverse in part.

BACKGROUND
A Cook County jury convicted petitioner of the murders of Candace Augustus and her 11-year-old son, Gregory. The same jury sentenced petitioner to death. This court affirmed petitioner's conviction and death sentence on direct appeal. People v. Fair, 159 Ill.2d 51, 201 Ill.Dec. 23, 636 N.E.2d 455 (1994). The United States Supreme *502 Court subsequently denied petitioner's petition for a writ of certiorari. Fair v. Illinois, 513 U.S. 1020, 115 S.Ct. 586, 130 L.Ed.2d 500 (1994).
Following petitioner's conviction, it was discovered that Cook County circuit court Judge Paul Foxgrover, who presided over petitioner's trial and sentencing, had engaged in extensive criminal conduct while on the bench between April 13, 1989, and July 9, 1991, both before and after petitioner's trial and sentencing. Judge Foxgrover sentenced criminal defendants to probation with a fine and/or restitution as a condition of probation and then converted fine or restitution checks to his own personal use on at least 50 separate occasions during this time period. Judge Foxgrover ultimately pleaded guilty to multiple counts of theft, official misconduct, forgery, obstruction of justice for attempting to cover up his criminal conduct and perjury for making false statements on official forms. All told, Judge Foxgrover pleaded guilty to 159 separate crimes.
Petitioner filed a post-conviction petition alleging that Judge Foxgrover's massive corruption violated petitioner's right to a fair trial guaranteed by the due process clauses of the United States and Illinois Constitutions. The circuit court granted the State's motion to dismiss the post-conviction petition without an evidentiary hearing, holding petitioner failed to establish any nexus between Judge Foxgrover's criminal conduct and petitioner's murder trial. Petitioner now appeals to this court.

STANDARD OF REVIEW
At the motion to dismiss stage in post-conviction proceedings, all well-pleaded facts that are not positively rebutted by the trial record are to be taken as true. The inquiry into whether a post-conviction petition sufficiently alleges a substantial violation of petitioner's constitutional rights does not require the trial court to engage in any fact-finding or credibility determinations. People v. Coleman, 183 Ill.2d 366, 385, 233 Ill.Dec. 789, 701 N.E.2d 1063 (1998). As a result, there is little justification for giving deference to the trial court's conclusions as to the sufficiency of the allegations in the post-conviction petition. Coleman, 183 Ill.2d at 388-89, 233 Ill.Dec. 789, 701 N.E.2d 1063. The standard of review for a trial court's decision to dismiss post-conviction claims without conducting an evidentiary hearing, therefore, is de novo. Coleman, 183 Ill.2d at 389, 233 Ill.Dec. 789, 701 N.E.2d 1063.

ANALYSIS

I. Petitioner's Due Process Claim
Petitioner first argues that he does not have to establish a nexus between Judge Foxgrover's criminal conduct and his murder trial. According to petitioner, Judge Foxgrover's corruption was so pervasive that there is no basis for presuming that he was impartial at petitioner's trial. We disagree. In People v. Titone, 151 Ill.2d 19, 175 Ill.Dec. 702, 600 N.E.2d 1160 (1992), the petitioner filed a post-conviction petition alleging he was denied a fair trial before an impartial tribunal. Petitioner alleged that the judge at his murder trial, Cook County circuit court Judge Thomas J. Maloney, agreed to accept a $10,000 bribe to acquit petitioner. Petitioner alleged that he was convicted either because his trial attorney failed to pay Judge Maloney the $10,000 bribe or because Judge Maloney accepted the bribe but convicted petitioner anyway in order to convince federal authorities investigating judicial corruption in Chicago that he did not accept a bribe. This court affirmed the dismissal of the post-conviction petition, holding that petitioner presented no evidence that Judge Maloney accepted or agreed to accept a bribe in petitioner's case. We also held that the fact that Judge Maloney was then under investigation in nonrelated cases arising out of his tenure as a Cook County circuit judge was not germane to the facts of that case. Titone, 151 Ill.2d at 30, 175 Ill.Dec. 702, 600 N.E.2d 1160. The *503 mere fact that Judge Maloney was implicated in accepting bribes in other nonrelated cases, we concluded, could not serve to taint all other decisions with which Judge Maloney was involved. Titone, 151 Ill.2d at 29, 175 Ill.Dec. 702, 600 N.E.2d 1160. Instead, we held that a petitioner who alleges that his trial judge's corruption violated his right to a fair trial must establish (1) a "nexus" between the judge's corruption or criminal conduct in other cases and the judge's conduct at petitioner's trial; and (2) actual bias resulting from the judge's extrajudicial conduct. Titone, 151 Ill.2d at 30-31, 175 Ill.Dec. 702, 600 N.E.2d 1160.
Petitioner argues that we dispensed with the nexus requirement in People v. Hawkins, 181 Ill.2d 41, 228 Ill.Dec. 924, 690 N.E.2d 999 (1998). Petitioner fundamentally misreads our opinion in Hawkins. Hawkins, like Titone, involved a post-conviction claim alleging Judge Maloney's corruption violated petitioners' right to a fair trial and required the reversal of the petitioners' murder convictions. Unlike this case, however, the petitioners presented evidence that Judge Maloney accepted a bribe at their murder trial and then returned the bribe when he suspected the FBI was investigating his conduct.
We stated in Hawkins:
"A fair trial in a fair tribunal is a basic requirement of due process. Bracy v. Gramley, 520 U.S. 899, 905, 117 S.Ct. 1793, 1797, 138 L.Ed.2d 97, 104 (1997); In re Murchison, 349 U.S. 133, 136, 75 S.Ct. 623, 625, 99 L.Ed. 942, 946 (1955). Fairness at trial requires not only the absence of actual bias but also the absence of the probability of bias. In re Murchison, 349 U.S. at 136, 75 S.Ct. at 625, 99 L.Ed. at 946. To this end, no person is permitted to judge cases in which he or she has an interest in the outcome. Bracy, 520 U.S. at 905, 117 S.Ct. at 1797, 138 L.Ed.2d at 104; In re Murchison, 349 U.S. at 136, 75 S.Ct. at 625, 99 L.Ed. at 946. `Every procedure which would offer a possible temptation to the average man as a judge to forget the burden of proof required to convict the defendant, or which might lead him not to hold the balance nice, clear and true between the state and the accused denies the latter due process of law.' Tumey v. Ohio, 273 U.S. 510, 532, 47 S.Ct. 437, 444, 71 L.Ed. 749, 758 (1927); see also Aetna Life Insurance Co. v. Lavoie, 475 U.S. 813, 822, 106 S.Ct. 1580, 1585, 89 L.Ed.2d 823, 833 (1986); Ward v. Village of Monroeville, 409 U.S. 57, 60, 93 S.Ct. 80, 83, 34 L.Ed.2d 267, 270-71 (1972).
Because our inquiry is limited to whether Maloney could have been tempted not to hold the balance between the parties `"`nice, clear and true'"' (Aetna Life Insurance Co., 475 U.S. at 822, 106 S.Ct. at 1585, 89 L.Ed.2d at 833; Ward, 409 U.S. at 60, 93 S.Ct. at 83, 34 L.Ed.2d at 271; Tumey, 273 U.S. at 532, 47 S.Ct. at 444, 71 L.Ed. at 758), defendants need not show actual bias by the trier of fact in order to be granted a new trial. As the United States Supreme Court stated in In re Murchison, 349 U.S. at 136, 75 S.Ct. at 625, 99 L.Ed. at 946, due process will sometimes `bar trial by judges who have no actual bias and would do their very best to weigh the scales of justice equally between the contending parties. But to perform its high function in the best way, "justice must satisfy the appearance of justice."'" Hawkins, 181 Ill.2d at 50-51, 228 Ill.Dec. 924, 690 N.E.2d 999.
This "appearance of justice" language in Hawkins did not, as petitioner suggests, eliminate the first prong of the test established in Titone. Hawkins simply clarified the second prong of the test by adding that a post-conviction petitioner need not prove actual bias if he can prove that the trial judge had a personal interest in the outcome of the trial. In such cases, we concluded, the appearance of justice requires reversal of petitioner's conviction and a new trial. Nothing in Hawkins, however, supports petitioner's argument *504 that the "appearance of justice" requires the reversal of a criminal conviction where the post-conviction petitioner alleging judicial bias has failed to establish any connection whatsoever between the judge's corruption or criminal conduct in other cases and the petitioner's trial. We therefore reaffirm our holding in Titone that in order to secure relief on a claim of judicial bias, a post-conviction petitioner must establish a nexus between a judge's corruption and the judge's conduct at petitioner's trial.[1]
Petitioner argues in the alternative that he has established a nexus between Judge Foxgrover's criminal conduct and his trial. Because we have determined to grant petitioner relief on a subsidiary claim related to this argument, however, we express no opinion on the merits of the argument itself. Petitioner asserts that, if he must prove a nexus between Judge Foxgrover's corruption and petitioner's trial, the circuit court erred when it denied petitioner's request for discovery to uncover the full extent of Judge Foxgrover's corruption. We agree.
The circuit court denied petitioner's discovery motion which sought production of the following evidence obtained by the Cook County State's Attorney's office during its investigation into Foxgrover's misconduct: "a lengthy confession by Judge Foxgrover, the interviews of numerous witnesses and the collection of substantial other material." Our review of the circuit court's ruling on petitioner's discovery request is complicated by the fact that petitioner has failed to include a copy of his discovery request in the record on appeal. An appellant has the burden to present a sufficiently complete record of the proceedings below to support a claim of error. Foutch v. O'Bryant, 99 Ill.2d 389, 391, 76 Ill.Dec. 823, 459 N.E.2d 958 (1984). In the absence of a complete record on appeal, it will be presumed that the order entered by the circuit court was in conformity with law and had a sufficient factual basis. Foutch, 99 Ill.2d at 392, 76 Ill.Dec. 823, 459 N.E.2d 958. Therefore, any doubts which may arise from the incompleteness of the record regarding the precise scope of petitioner's discovery request will be resolved against petitioner. Foutch, 99 Ill.2d at 392, 76 Ill.Dec. 823, 459 N.E.2d 958. Since a complete review of the circuit court's ruling on petitioner's discovery request is impossible in this case, we limit our review of the discovery request to the evidence specifically identified in petitioner's appellant's brief: Judge Foxgrover's confession and any interviews of witnesses conducted during the course of the investigation into Judge Foxgrover's criminal conduct.
The discovery rules for neither civil nor criminal cases apply to proceedings under the Post-Conviction Hearing Act. People ex rel. Daley v. Fitzgerald, 123 Ill.2d 175, 181-83, 121 Ill.Dec. 937, 526 N.E.2d 131 (1988). Nonetheless, the circuit court has inherent discretionary authority to order discovery in post-conviction proceedings. Daley, 123 Ill.2d at 183, 121 Ill.Dec. 937, 526 N.E.2d 131. Circuit courts, however, must exercise this authority with caution because post-conviction proceedings afford only limited review of constitutional claims not presented at trial, and there is a potential for abuse of the discovery process in post-conviction proceedings. Daley, 123 Ill.2d at 183, 121 Ill.Dec. 937, 526 N.E.2d 131. As a result, the circuit court should allow discovery only after the moving party demonstrates "good cause" for a discovery request. Daley, 123 Ill.2d at 183, 121 Ill.Dec. 937, 526 N.E.2d 131. We will not disturb a circuit court's denial of a request for discovery in post-conviction proceedings absent an *505 abuse of discretion. See People v. Henderson, 171 Ill.2d 124, 156, 215 Ill.Dec. 147, 662 N.E.2d 1287 (1996).
In Bracy v. Gramley, 520 U.S. 899, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997), the petitioner was tried, convicted and sentenced to death by Judge Maloney. After a federal investigation into judicial corruption in Chicago, Maloney was convicted of taking bribes from defendants in criminal cases around the time of the petitioner's trial. See United States v. Maloney, 71 F.3d 645 (7th Cir.1995). Although Maloney did not take a bribe in the petitioner's case, petitioner alleged in a federal habeas corpus petition that Maloney had a personal interest in his conviction which violated petitioner's right to a fair trial guaranteed by the due process clause of the fourteenth amendment. According to petitioner, his conviction would deflect suspicion that Maloney was taking bribes in other murder cases. In support of a discovery request for the sealed transcript of Maloney's trial, access to the prosecution's materials in Maloney's criminal case, and the opportunity to depose persons associated with Maloney, petitioner presented evidence that his murder trial was sandwiched tightly between other murder trials in which Maloney accepted bribes. Petitioner also presented evidence that Maloney offered bribes to judges in cases while he was a practicing criminal defense attorney and that at least one of his colleagues in private practice actively assisted in these bribes. Petitioner's trial attorney was another former associate of Maloney from private practice whom Maloney appointed to represent petitioner. This attorney announced that he was ready for trial only a few weeks after he was appointed, and the attorney did not request additional time to prepare penalty phase evidence after the State announced its intention to seek the death penalty. These procedural irregularities, petitioner argued, raised the possibility that Maloney appointed his former colleague from private practice to represent petitioner in order to quickly secure a conviction, which would deflect attention away from the other murder trials fixed by Maloney. The United States Supreme Court held that petitioner's allegations established "good cause" for his discovery request to support his claim that Maloney was actually biased in his case. Bracy, 520 U.S. at 908, 117 S.Ct. at 1799, 138 L.Ed.2d at 106.
The allegations in the post-conviction petition in this case lack the specificity of the allegations in Bracy. The petitioner in Bracy, however, had access to public sources of information regarding Judge Maloney's corruption, while public sources of information regarding Judge Foxgrover's corruption are unavailable to the petitioner in this case. Judge Maloney was convicted after a trial in federal court. Thus, the petitioner in Bracy had a wealth of information from the record of Judge Maloney's trial upon which to base his habeas corpus claim. Judge Foxgrover, however, pleaded guilty, thus depriving the petitioner in this case of a valuable public source of information regarding Judge Foxgrover's corruption. All of the evidence regarding Judge Foxgrover's criminal conduct remains in the exclusive control of the State. It would be virtually impossible for the petitioner in this case to establish a nexus between Judge Foxgrover's criminal conduct and petitioner's murder trial without access to the evidence possessed by the State.
The State argues that petitioner has not established good cause for his discovery request because nothing in the post-conviction petition suggests that a nexus exists. The State's argument, however, puts petitioner in an impossible dilemma. According to the State, petitioner is entitled to seek out evidence that there is a nexus between Judge Foxgrover's criminal conduct and petitioner's trial only if he already possesses such evidence. The State also argues that allowing petitioner to conduct discovery will further delay the adjudication of this case. The State undoubtedly has an interest in the finality of *506 criminal convictions, but there are other equally compelling interests at stake in this case. Judge Foxgrover's extensive criminal conduct while on the bench and utter disregard for his oath has tainted the judicial system of this state. The finality of criminal convictions is a hollow achievement if the integrity of the judicial system which produces these convictions is open to question. Petitioner is entitled to an opportunity to find and present whatever evidence there may be which connects Judge Foxgrover's criminal conduct to his ability to be an impartial judge at petitioner's murder trial.

II. Petitioner's Ineffective Assistance of Counsel Claims
Petitioner next argues that his trial counsel was ineffective for failing to prevent Cameron Forbes, a supervisor at the Department of Corrections records office, from testifying at petitioner's sentencing hearing regarding petitioner's prison record. According to petitioner, the record of petitioner's rules violations in prison is unreliable and Forbes was not qualified to testify regarding conclusions about petitioner's character contained in prison reports.
The Post-Conviction Hearing Act cannot be used to obtain another hearing on a constitutional claim which has already been given full review by this court on direct appeal. People v. Emerson, 153 Ill.2d 100, 106, 180 Ill.Dec. 46, 606 N.E.2d 1123 (1992), quoting People v. Cox, 34 Ill.2d 66, 67-68, 213 N.E.2d 524 (1966). Rulings on issues raised on direct appeal, therefore, are res judicata. Emerson, 153 Ill.2d at 106, 180 Ill.Dec. 46, 606 N.E.2d 1123, quoting People v. Ruiz, 132 Ill.2d 1, 9, 138 Ill.Dec. 201, 547 N.E.2d 170 (1989). A post-conviction petitioner cannot avoid the bar of res judicata simply by rephrasing claims raised on direct appeal. Emerson, 153 Ill.2d at 106, 180 Ill.Dec. 46, 606 N.E.2d 1123.
On direct appeal, petitioner argued that Forbes' testimony gleaned from petitioner's prison records was unreliable and inadmissible. This court rejected petitioner's argument and held that petitioner's prison records were properly admitted at his sentencing hearing. Fair, 159 Ill.2d at 89-90, 201 Ill.Dec. 23, 636 N.E.2d 455. Petitioner's ineffective assistance of counsel claim regarding Forbes' testimony is simply a rephrasing of his argument on direct appeal. Petitioner's claim, therefore, is barred by res judicata.
Petitioner also argues that his trial counsel was ineffective for failing to correct the false impression created by the State at petitioner's sentencing hearing that petitioner is an older individual who manipulates youths to commit crimes. According to petitioner, the State argued at the sentencing hearing that petitioner was with "two juveniles" when he committed an armed robbery in 1966. Petitioner argues that his trial counsel should have pointed out that petitioner was only 18 years old at the time of the armed robbery and that the "two juveniles" were 17 years old, only one year younger than petitioner. The State responds that petitioner waived this claim because he could have raised it on direct appeal but failed to do so. We disagree. Petitioner did not waive this claim because he asserts in his post-conviction petition that his appellate counsel was ineffective for failing to raise the claim on direct appeal. This ineffective assistance of appellate counsel argument is a well-recognized exception to the waiver doctrine in post-conviction proceedings. See People v. Turner, 187 Ill.2d 406, 413, 241 Ill.Dec. 596, 719 N.E.2d 725 (1999).
Petitioner's claim, however, fails on the merits. In order to show that his trial counsel was ineffective at his death sentence hearing, petitioner must prove that his counsel's representation was deficient and that there is a reasonable probability that, but for counsel's deficient conduct, the sentencer would have concluded that the balance of aggravating and mitigating circumstances did not warrant death. People v. Hampton, 149 Ill.2d 71, *507 109, 171 Ill.Dec. 439, 594 N.E.2d 291 (1992), citing Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Even if we assume that petitioner has shown that his trial counsel was deficient for failing to correct this false impression, we hold that petitioner has failed to demonstrate that he suffered any prejudice from this deficiency. As this court noted on direct appeal, the aggravating and mitigating evidence at petitioner's sentencing hearing was not closely balanced. Fair, 159 Ill.2d at 88, 201 Ill.Dec. 23, 636 N.E.2d 455. Petitioner brutally murdered Candace Augustus and her 11-year-old son, Gregory, by bludgeoning them to death with a baseball bat. Petitioner has an extensive history of criminal behavior, and petitioner has failed dismally at adjusting to incarceration. In light of this compelling aggravating evidence, trial counsel's failure to correct a false impression regarding one of petitioner's prior convictions had no demonstrable effect on the outcome of petitioner's sentencing hearing. Petitioner has failed to prove that there is a reasonable probability that, but for his counsel's deficient performance, the outcome of his sentencing hearing would have been different.
Petitioner next argues that the "other instances of ineffective assistance of counsel as asserted in the post-conviction petition are sufficient to require an evidentiary hearing." Petitioner, however, provides no argument in support of this contention, nor does he provide any citations to relevant legal authority in support of these claims. As a result, these remaining ineffective assistance of counsel claims fail to satisfy the requirements of Supreme Court Rule 341(e)(7) (134 Ill.2d R. 341(e)(7)) and are waived.[2]

III. Petitioner's Challenge to the Constitutionality of the Death Penalty Statute
Petitioner next argues that section 9-1(b)(7) of the death penalty statute, which provides that a defendant is eligible for the death penalty if "the murdered individual was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty" (Ill.Rev.Stat.1987, ch. 38, par. 9-1(b)(7)), is unconstitutionally vague. Petitioner's argument is barred by res judicata because this argument was raised, and rejected by this court, on direct appeal. Fair, 159 Ill.2d at 80, 201 Ill.Dec. 23, 636 N.E.2d 455 (holding that section 9-1(b)(7) is not unconstitutional on its face because it "specifically describes the conduct which qualifies an accused for the death penalty and is not susceptible to arbitrary application").

CONCLUSION
For the reasons stated above, the judgment of the circuit court of Cook County dismissing petitioner's post-conviction petition without an evidentiary hearing is affirmed in part and reversed in part. The circuit court's denial of petitioner's discovery request with respect to Judge Foxgrover's confession and any interviews of witnesses conducted during the course of the investigation into Judge Foxgrover's criminal conduct is reversed, and the circuit court is directed to enter an order that these materials be made available to petitioner. After petitioner has been provided with these items and has had an opportunity to use them in support of his claim of a nexus between Judge Foxgrover's criminal conduct and petitioner's case, the circuit court is directed to reconsider and enter a new ruling on petitioner's allegation that Judge Foxgrover's criminal conduct violated his due process right to a fair trial.
The remainder of the circuit court's judgment is affirmed, and the cause is remanded to the circuit court for further proceedings consistent with this opinion.
*508 Judgment affirmed in part and reversed in part; cause remanded.
Chief Justice HARRISON, specially concurring:
I agree with the result reached by the majority in this case. The circuit court should not have denied Fair's discovery request. Fair is entitled to find and present whatever evidence there may be to establish that Judge Foxgrover's criminal conduct had an effect on his impartiality at Fair's trial.
I write separately because I would go beyond the majority's holding and declare this state's death penalty law unconstitutional. For the reasons set forth in my partial concurrence and partial dissent in People v. Bull, 185 Ill.2d 179, 235 Ill.Dec. 641, 705 N.E.2d 824 (1998), the law violates the eighth and fourteenth amendments to the United States Constitution (U.S. Const., amends. VIII, XIV) and article I, section 2, of the Illinois Constitution (Ill. Const. 1970, art. I, § 2). It is therefore void and unenforceable. Under these circumstances, Fair's death sentence should not be allowed to stand regardless of the outcome of the proceedings on remand. Even if Fair's post-conviction claims prove unfounded, his sentence of death should be vacated and he should be sentenced to a term of imprisonment. Ill.Rev.Stat. 1987, ch. 38, par. 9-1(j).
NOTES
[1]  This reading of Hawkins also comports with the United States Supreme Court's understanding of the elements of a judicial bias claim. See Bracy v. Gramley, 520 U.S. 899, 904-05, 117 S.Ct. 1793, 1797, 138 L.Ed.2d 97, 104 (1997) (holding due process clause requires a "fair trial in a fair tribunal" before "a judge with no actual bias against the defendant or interest in the outcome of his particular case").
[2]  Petitioner argues in summary fashion later in his appellant's brief that there are other issues in the post-conviction petition which merit an evidentiary hearing, but these claims are waived for the same reason.
