
608 So.2d 778 (1992)
Harry Franklin PHILLIPS, Appellant,
v.
STATE of Florida, Appellee.
No. 75598.
Supreme Court of Florida.
September 24, 1992.
Rehearing Denied December 24, 1992.
*779 Larry Helm Spalding, Capital Collateral Representative (CCR), Jerrel E. Phillips, Asst. CCR, Office of Capital Collateral Representative, Tallahassee, and Billy H. Nolas and Julie D. Naylor, Sp. Asst. CCR, Ocala, for appellant.
Robert A. Butterworth, Atty. Gen. and Ralph Barreira, Asst. Atty. Gen., Miami, for appellee.
PER CURIAM.
Harry Franklin Phillips, a prisoner under sentence of death, appeals from the circuit court's denial of his petition under Florida Rule of Criminal Procedure 3.850. We have jurisdiction under article V, section 3(b)(1) of the Florida Constitution.
Phillips was convicted of the 1982 murder of Bjorn Svenson, a parole supervisor. The jury recommended a death sentence by a vote of seven to five, and the judge followed this recommendation. This Court affirmed the conviction and sentence on appeal. Phillips v. State, 476 So.2d 194 (Fla. 1985). After his first death warrant was signed, Phillips filed a petition for habeas corpus, alleging a violation of his rights under Caldwell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985). The petition was denied by this Court as procedurally barred. Phillips v. Dugger, 515 So.2d 227 (Fla. 1987). Phillips *780 then filed this 3.850 motion. An evidentiary hearing was held, and the circuit court denied relief on all claims.
We first address the claims Phillips raises alleging error in the guilt phase of his trial. Much of the State's evidence at trial consisted of the testimony of inmates who had been in a cell with Phillips. These inmates testified that Phillips admitted his guilt to them, and each supplied details of the crime as Phillips portrayed it to them  details which presumably only the killer would know.
Phillips contends that the State failed to disclose the nature or extent of the benefits offered to these inmates in exchange for their testimony, violating his rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). However, before trial, Phillips was allowed to depose the prosecutor in this case, David Waksman. He also took the depositions of the inmates themselves and of the lead detective, Greg Smith. Through these depositions, Phillips learned that the inmates had been told that Waksman would write a letter informing the relevant authority  the parole board for those inmates who were serving prison sentences and the sentencing judge for those inmates who had not yet gone to trial  of their cooperation in the case. In addition, one inmate, Malcolm Watson, was promised that he would be given a polygraph test regarding his crime, and if he passed it his sentencing judge would be so informed. These promises were brought out on cross-examination of the inmates at trial.
Phillips now contends that the inmates were promised much more than was actually disclosed. In support of this claim, he introduced at the postconviction hearing documents showing that Waksman and Smith were involved in various activities in aid of the inmates after trial. For example, Waksman became involved in plea negotiations which ultimately resulted in a lenient sentence of five years' probation for Larry Hunter.
In rebutting this allegation, the State presented Waksman as a witness, who explained that he did in fact do more than simply write letters for some of the inmates. Because they had been such a help to the case and had gone through such pains to testify, including spending more time in jail while their own trials were postponed and being subjected to beatings and threats from other prisoners, Waksman decided to aid these inmates in whatever ways he could. However, he did not inform the inmates that he was going to do anything other than write letters, and in fact he himself had no idea to what extent he would end up helping them.[1]
Phillips also introduced check stubs showing that the inmates were in fact given reward money after trial. However, Smith and Waksman explained that this money was provided by the Florida Police Benevolent Association, a private organization, that they themselves were unaware of the reward until shortly before trial, and that they never told the inmates about the money until after they testified. Accordingly, although the inmates were ultimately given reward money by an outside organization, they were not aware of the possibility of a reward until after trial, and it therefore could not have provided any incentive for them to testify.
Finally, Phillips presented the testimony of William Farley, who stated that he lied on the stand at trial, that Phillips had never in fact confessed to him, that all the information about the crime was provided to him by the police, and that he perjured himself on the stand after being promised freedom and reward money. A similar claim was made as to the testimony of Larry Hunter. While Hunter himself refused to testify on grounds of self-incrimination, the parties stipulated to the consideration of his affidavit. Waksman and Smith denied these allegations. The circuit *781 court found this evidence to be completely unbelievable, and we find competent, substantial evidence to support this finding. Accordingly, we reject Phillips' Brady claim.
Phillips next claims that various witnesses lied on the stand at trial and the State failed to correct the false testimony, in violation of Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). In order to prevail on this claim, Phillips must demonstrate: (1) the testimony was false; (2) the prosecutor knew the testimony was false; and (3) the statement was material. Routly v. State, 590 So.2d 397, 400 (Fla. 1991).
Phillips first alleges that William Scott was a police informant at the time Phillips confessed to him, yet he stated on the witness stand that he was not a police agent. The fact that Scott had been a paid informant for the federal government and had aided one of the detectives in the Metro-Dade police department was well known to the defense through pretrial depositions of Scott and Detective Smith and was brought out on cross-examination at trial. Scott's statement that he was not a police agent is attributable to the ambiguity of the term "agent." Scott was on the federal government payroll at the time of trial and was assigned an informant number for the federal authorities; he did not, at that time, have an informant number for the Metro-Dade police, and therefore evidently did not believe that he was an agent for that department. Even at the postconviction hearing, Scott seemed confused over whether he was an informant for Metro-Dade. Ambiguous testimony does not constitute false testimony for the purposes of Giglio. Routly, 590 So.2d at 400.
Phillips also alleges that William Farley lied when he stated that the tape was started immediately when he gave his tape-recorded statement to the police; actually, a pre-interview was conducted which lasted approximately one and one-half hours. We find this misstatement to be immaterial. Further, the statement could have been corrected by the defense, had it been important, since the defense was aware of the pre-interview from Detective Smith's pretrial deposition.
Finally, Phillips contends that both Farley and Watson lied about their criminal records. While we agree that statements made by these witnesses regarding their records were incorrect, we find that there is no reasonable probability that the false testimony affected the judgment of the jury. The jury was made aware that these witnesses were convicted felons; the admission of an additional conviction or probationary sentence would have added virtually nothing to further undermine their credibility.
In a related claim, Phillips argues that the State used the jailhouse informants to elicit testimony from Phillips after he asserted his right to counsel, violating his rights under United States v. Henry, 447 U.S. 264, 100 S.Ct. 2183, 65 L.Ed.2d 115 (1980). This claim is without merit, as Phillips has made no showing that the informants were state agents when they talked with him,[2] that they in any way attempted to elicit information about the crimes, or that the State had anything to do with placing these persons in a cell with Phillips in order to obtain information.
Phillips next argues that his trial counsel was ineffective at the guilt phase. In order to prevail on this claim, Phillips must demonstrate that counsel's performance was deficient and that there is a reasonable probability that the result of the proceeding would have been different absent the deficient performance. Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
Phillips bases his claim on several alleged actions which counsel failed to take. First, Phillips contends that counsel should have obtained a competency evaluation before trial. In support of this allegation, *782 Phillips presented the testimony of two forensic psychology experts, who stated that Phillips was not competent at the time of his trial. In rebutting this claim, the State presented the testimony of two experts who opined that Phillips was competent at trial, and the testimony of Phillips' counsel, who stated that there was absolutely no reason to doubt Phillips' competence at the time of trial.[3] The State also presented notes and letters written by Phillips at the time of trial which indicated overall intellectual functioning and an understanding of the case against him. The circuit court found that Phillips was competent at trial and that counsel was not ineffective for failing to have his competency evaluated. We find competent, substantial evidence to support the circuit court's finding on this issue.
Phillips next claims that counsel was ineffective for failing to investigate the jailhouse informants, for failing to file a motion to suppress, for failing to move for a change of venue, for failing to conduct an appropriate voir dire, for failing to obtain or consult with experts, for failing to object to Phillips' absence from certain proceedings, for failing to adequately cross-examine witnesses, and for failing to object to hearsay, lay opinions, and improper comments during the prosecutor's closing argument. We find these claims to be conclusory and summarily reject them. Many of these claims are exactly the type of hindsight second-guessing that Strickland condemns, and even those matters asserted as significant "omissions" would have been mere exercises in futility, with no legal basis. Accordingly, having found that Phillips has demonstrated neither deficient performance nor prejudice, we reject his claim that trial counsel was ineffective at the guilt phase.
We turn now to Phillips' claims regarding the sentencing phase of his trial. Phillips first argues that his trial counsel was ineffective at sentencing. Counsel testified at the postconviction hearing that he did virtually no preparation for the penalty phase. The only testimony presented in mitigation was that of Phillips' mother, who testified that Phillips was a good son who tried to help her when he was not in prison. The State has conceded that counsel's performance was deficient at the penalty phase, but contends that the deficient performance did not prejudice Phillips, as he would have been sentenced to death anyway. The circuit court agreed with the State.
At the postconviction proceeding, Phillips introduced a large amount of mitigating evidence through the testimony of relatives and friends of the family, who described Phillips' poor childhood, and through the testimony of expert witnesses, who described Phillips' mental and emotional deficiencies.
Phillips' mother, brother, and sister testified that Phillips grew up in poverty. His parents were migrant workers who often left the children unsupervised. Phillips' father physically abused him, and physically abused Phillips' mother in front of the children. Phillips was a withdrawn, quiet child with no friends. When he was thirteen or fourteen, Phillips was shot in the head and taken to the hospital.
The State argues that this childhood evidence is entitled to little weight, since Phillips was thirty-six years old at the time he committed this crime and had numerous chances to rehabilitate himself by then. Although it is true that this evidence is far less compelling as mitigation in light of Phillips' age, this does not change the fact that it was relevant, admissible evidence that should have been presented to the jury. It cannot be seriously argued that the admission of this evidence could have in any way affirmatively damaged Phillips' case.
More compelling evidence was presented by Phillips' experts. These experts testified that Phillips is emotionally, intellectually, *783 and socially deficient, that he has lifelong deficits in his adaptive functioning, that he is withdrawn and socially isolated, that he has a schizoid personality, and that he is passive-aggressive. Phillips' IQ was found to be between seventy-three and seventy-five, in the borderline intelligence range. Both experts concluded that Phillips falls under the statutory mitigating circumstances of extreme emotional disturbance and an inability to conform his conduct to the requirements of the law.[4] They also opined that Phillips did not have the capacity to form the requisite intent to fall under the aggravating factors of cold, calculated, and premeditated or heinous, atrocious, or cruel.[5]
Again, the State contends that this mitigation is not sufficiently compelling to demonstrate prejudice. However, this testimony provides strong mental mitigation and was essentially unrebutted. The testimony of the State experts related solely to the issue of competency. While these experts testified that they did not believe Phillips had significant mental or emotional disorders, they offered no opinion as to the applicability of the statutory mental mitigators, and even these experts agreed that Phillips' intellectual functioning is at least low average and possibly borderline retarded. Accordingly, even giving full credit to the testimony of the State's experts there was significant, unrebutted mental mitigation which should have been considered by the jury.[6]
The jury vote in this case was seven to five in favor of a death recommendation. The swaying of the vote of only one juror would have made a critical difference here. Accordingly, we find that there is a reasonable probability that but for counsel's deficient performance in failing to present mitigating evidence the vote of one juror would have been different, thereby changing the jury's vote to six to six and resulting in a recommendation of life reasonably supported by mitigating evidence. Having demonstrated both deficient performance and prejudice, Phillips is entitled to relief on his claim of ineffective assistance of counsel at the sentencing phase of his trial. Given our resolution of this issue, it is unnecessary for us to address the remainder of Phillips' claims of error in his sentencing.[7]
For the foregoing reasons, the circuit court's order is affirmed in part and reversed in part, the sentence of death is vacated, and the case is remanded for a new sentencing proceeding before a jury.
It is so ordered.
BARKETT, C.J., and OVERTON, GRIMES, KOGAN and HARDING, JJ., concur.
SHAW, J., concurs in result only.
McDONALD, J., concurs in part and dissents in part with an opinion.
McDONALD, Justice, concurring in part, dissenting in part.
I concur in the denial of relief to Phillips on the guilt phase of his trial, but would also deny relief on the sentence. I agree with the trial judge when he determined:
Based on the facts surrounding the murder, this Court finds that there is no reasonable probability that the evidence of a troubled childhood and limited mental capacity would have altered the jury's decision and certainly not this Court's decision. Since Phillips has not established prejudice, he is not entitled to relief on this claim.
NOTES
[1]  Phillips also cites several examples of good fortune which befell the inmates after they testified against him. For example, Malcolm Watson's life sentence was vacated, William Farley received early parole, and assault charges against William Scott were dropped. However, Phillips submitted no proof that these events were causally connected to the inmates' testimony at trial or that they took place in fulfillment of promises by the State.
[2]  Although William Scott was a state agent when he attempted to elicit information from Phillips' family, this action in no way implicated Phillips' rights. The circumstances of this incident were not hidden by the State, as Scott discussed the incident in his pretrial deposition.
[3]  Phillips places much emphasis on counsel's statements that Phillips was an "idiot." Counsel explained that this statement did not reflect his feelings about Phillips' mental capacity, but rather about his tendency to take actions which sabotaged his own case, such as bragging about the crime to other inmates.
[4]  § 921.141(6)(b), (f), Fla. Stat. (1981).
[5]  § 921.141(5)(i), (h), Fla. Stat. (1981).
[6]  While the circuit judge ruled against Phillips on the competency claim, he never found as a factual matter that no mental mitigation was established.
[7]  Phillips argues: 1) comments by the court and prosecutor diminished the jury's sense of responsibility for the sentencing decision; 2) trial counsel was ineffective for failing to object to a jury instruction which shifted the burden of proof at sentencing to Phillips; and 3) trial counsel was ineffective for failing to object to inconsistent jury instructions regarding the vote necessary for a life recommendation.
