
927 S.W.2d 579 (1995)
Gary Bradford CONE, Appellant,
v.
STATE of Tennessee, Appellee.
Court of Criminal Appeals of Tennessee, at Jackson.
March 22, 1995.
Permission to Appeal Denied March 4, 1996.
*580 Stephen R. Glassroth, Glassroth & Associates, P.C., Montgomery, Alabama, Kemper B. Durand, Thomason, Hendrix, Harvey, Johnson & Mitchell, Memphis, for Appellant.
Charles W. Burson, Attorney General and Reporter, Rebecca L. Gundt, Assistant Attorney General, Criminal Justice Division, Nashville, John W. Pierotti, District Attorney General, Kevin Rardin, Asst. Dist. Attorney General, Memphis, for Appellee.
Permission to Appeal Denied by Supreme Court March 4, 1996.

OPINION
SUMMERS, Judge.
The appellant, Gary Bradford Cone, was convicted of murder and sentenced to death in 1982. After unsuccessfully appealing to the Tennessee Supreme Court, the appellant filed a petition for post-conviction relief. Appellant's first petition was denied, and this Court affirmed the denial. Appellant then filed a second petition, which was dismissed by the trial court. On appeal, this Court remanded the trial court's denial of the appellant's second post-conviction petition in order to give the appellant an opportunity to rebut the presumption of waiver arising from the previous post-conviction proceedings. Appellant filed a lengthy factual affidavit concerning waiver and, following oral argument on the waiver issue, the trial court found that all of the issues raised by the appellant's amended second petition were either previously determined or waived. Accordingly, the trial court dismissed the appellant's second petition. The appellant now appeals the trial court's denial of his second post-conviction petition, presenting for our review the related issues of whether the trial court's dismissal was either premature or incorrect. Having carefully considered both issues, we find them to be without merit and affirm the judgment of the trial court.

ANALYSIS
Appellant contends that the trial court's dismissal of his second petition was premature, because the state had not adequately responded to the petition as amended and because the trial court declined to hold an evidentiary hearing.[1] The appellant's position on this issue is based on the Tennessee Supreme Court cases of Swanson v. State, 749 S.W.2d 731 (Tenn. 1988), and Allen v. State, 854 S.W.2d 873 (Tenn. 1993). In both Swanson and Allen, pro se post-conviction petitions were summarily dismissed upon the state's motion without appointment of counsel or an evidentiary hearing. The cases cited by the appellant are of limited relevance where, as here, the post-conviction petitioner had the benefit of appointed counsel to review and amend his original pro se petition. Furthermore, Swanson and Allen recognized that dismissal without an evidentiary hearing is proper where the petition fails to state a "colorable claim for relief," Allen v. State, 854 S.W.2d 873, 876, or where the claims in the petition are "conclusively incorrect." Swanson v. State, 749 S.W.2d 731, 736. Our conclusion as to the timeliness of the trial court's dismissal is therefore dependent on our resolution of the substantive issues of waiver and previous determination.
Grounds for relief which have been previously determined or waived are not cognizable in a post-conviction action. T.C.A. § 40-30-111 *581 (1990). Tennessee Code Annotated Section 40-30-112 (1990) provides as follows:
A ground for relief is "previously determined" if a court of competent jurisdiction has ruled on the merits after a full and fair hearing.
A ground for relief is "waived" if the petitioner knowingly and understandingly failed to present it for determination in any proceeding before a court of competent jurisdiction in which the ground could have been presented.
There is a rebuttable presumption that a ground for relief not raised in any such proceeding which was held was waived.
The trial court, in memorandum findings of fact and conclusions of law, addressed the fifty-two separate grounds alleged by the appellant as a basis for post-conviction relief. Had Judge Williams not provided this Court with such an exemplary and meticulous treatment of the appellant's petition, our task in reviewing the relevant issues would have been difficult if not insurmountable.
In post-conviction proceedings, the petitioner has the burden of proving the allegations in his petition by a preponderance of the evidence. McBee v. State, 655 S.W.2d 191, 195 (Tenn. Crim. App. 1983). Furthermore, the findings of the trial court in post-conviction hearings are conclusive on appeal unless the evidence preponderates against the judgment. State v. Buford, 666 S.W.2d 473, 475 (Tenn. Crim. App. 1983); Clenny v. State, 576 S.W.2d 12, 14 (Tenn. Crim. App. 1978).
The trial court found that most of the appellant's stated grounds for relief, in addition to being repetitious and cumulative, were previously determined either on direct appeal or in the appellant's first petition. The trial court also noted that many of the appellant's "grounds" are merely conclusory allegations which fail to state a constitutional deprivation and are therefore not cognizable in a post-conviction action.[2] Finally, the trial court found that the appellant had failed to rebut the presumption of waiver which would preclude the consideration of any new grounds raised in the appellant's petition.
The appellant's second petition contains the following blanket statement on the issue of waiver:
The above claims were not raised previously either due to the law regarding the claim not being established at the time, ineffective assistance of counsel, the novelty of the claim or counsel's failure to apprise petitioner of the claim or its relevance to his case. Because of this, the petitioner himself has never had an opportunity before now to either raise these claims or waive them. Neither petitioner nor any person previously appointed to represent petitioner has knowingly and understandingly failed to raise any and all such claims earlier.
The appellant contends that this statement alone is sufficient to rebut the presumption of waiver and that the trial court's dismissal of his second petition was therefore incorrect.
As for the appellant's claim that some of the issues raised in his second petition were "novel" or that the law concerning some issues was uncertain, we find, as did the trial court, that the appellant has failed to present any support for this vague and conclusory statement. Furthermore, because the appellant did not address the issue of "new law" in his brief or on oral argument to this court, the issue is waived. See Tenn. Rules of Crim.App.Rule 10(b); T.R.A.P.Rule 27(a)(7); State v. Chance, 778 S.W.2d 457, 462 (Tenn. Crim. App. 1989).
In his first post-conviction petition, the appellant presented five factual allegations to support his constitutional claim of ineffective assistance of counsel. His second petition, on the other hand, listed thirty-five separate deficiencies in his trial counsel's performance. The trial court found that ineffective assistance of counsel is a single "ground for relief" as contemplated by the statute, see T.C.A. § 40-30-111, and that the issue of ineffective assistance of counsel issue *582 was therefore previously determined. We agree with the trial court. A petitioner may not relitigate a previously determined issue by presenting additional factual allegations. We should not encourage post-conviction petitioners to invent new facts to revive an issue which was unfavorably decided, nor should we allow petitioners to "sandbag" by reserving factual claims until their second or third petition.
Finally, the appellant maintains that he did not waive any issues "knowingly and understandingly" as required by the statute. See T.C.A. § 40-30-112(b)(1). The trial court found that the appellant's mere statement that he did not understand the issues or appreciate the significance of them was insufficient, without further explanation, to rebut the presumption of waiver. Parenthetically, the trial court noted that the appellant was neither illiterate nor unsophisticated. In fact, the appellant graduated with honors from the University of Arkansas and had been accepted for admission into law school after scoring in the ninety-sixth percentile on his law school admission test.
We must agree with the trial court that the appellant should not be able to extend the post-conviction process and delay the administration of justice ad infinitum by filing subsequent petitions which disingenuously claim that the grounds asserted were unknown to the appellant when his previous petition was filed. As Justice Kennedy wrote for the United States Supreme Court in McCleskey v. Zant, 499 U.S. 467, 111 S.Ct. 1454, 113 L.Ed.2d 517 (1991), "[p]erpetual disrespect for the finality of convictions disparages the entire criminal justice system." Id. at 492, 111 S.Ct. at 1469. Our own Tennessee Supreme Court observed in 1972:
There must be a finality to all litigation, criminal as well as civil. The courts, the executive branch of government, the legal profession, and the public have been seriously inconvenienced by the prosecutions of baseless habeas corpus and post-conviction proceedings. Defendants to criminal prosecutions, like parties to civil suits, should be bound by the judgments therein entered. When they fail to make timely objections to errors of the courts they must not be allowed at later times of their own choosing  often perhaps, after witnesses against them have become unavailable  to assert those grounds in post-conviction actions.
Arthur v. State, 483 S.W.2d 95, 97 (Tenn. 1972).

CONCLUSION
We conclude that the appellant failed to rebut the presumption of waiver as to all claims raised in his second petition for post-conviction relief which had not been previously determined. The trial court's decision to dismiss the appellant's petition without an evidentiary hearing was neither improper nor premature. The judgment of the trial court is therefore:
AFFIRMED.
The appellant's sentence of death by electrocution is set for July 1, 1995, unless otherwise stayed by appropriate authority.
PEAY and HAYES, JJ., concur.
NOTES
[1]  The appellant argues that in our previous opinion, Cone v. State, C.C.A. No. 48, 1991 WL 77535 (Tenn. Crim. App. May 15, 1991), we remanded to the trial court for an evidentiary hearing. In that opinion, we held only that the appellant was entitled to an opportunity to rebut the presumption of waiver. Id. We did not intend to require the trial court to conduct an evidentiary hearing.
[2]  Post-conviction relief will only be granted where a defendant's conviction or sentence is either void or voidable due to the abridgement of a constitutional right. T.C.A. § 40-30-105 (1990).
