636 So.2d 1321 (1994)
Oscar TORRES-ARBOLEDA, Petitioner,
v.
Richard L. DUGGER, etc., Respondent.
Oscar Torres-Arboleda, Appellant,
v.
STATE of Florida, Appellee.
Nos. 75751, 79246.
Supreme Court of Florida.
April 21, 1994.
Rehearing Denied June 6, 1994.
Michael J. Minerva, Capital Collateral Representative, and Stephen M. Kissinger, Asst. Capital Collateral Representative, Office of the Capital Collateral Representative, Tallahassee, for petitioner-appellant.
Robert A. Butterworth, Atty. Gen., and Robert J. Landry, Asst. Atty. Gen., Tampa, for respondent-appellee.
PER CURIAM.
Oscar Torres-Arboleda, a prisoner under sentence of death, seeks postconviction relief. He appeals the trial court's denial of his Florida Rule of Criminal Procedure 3.850 motion for postconviction relief and petitions this Court for a writ of habeas corpus. We have jurisdiction pursuant to article V, sections 3(b)(1) and (9) of the Florida Constitution. We reverse the trial court's order denying rule 3.850 relief because we find that Torres-Arboleda was denied effective assistance of counsel during the penalty phase of his trial. However, we deny Torres-Arboleda's petition for a writ of habeas corpus.
Torres-Arboleda was convicted of first-degree murder and attempted armed robbery for the 1981 homicide of Tampa resident Patricio Lorenzo. The jury recommended life imprisonment by a vote of seven to five. The trial judge overrode the jury's recommendation and imposed a death sentence, based upon his finding of two aggravating circumstances (previous felony conviction and committed while attempting to commit a robbery) and no mitigating circumstances. On direct appeal, this Court affirmed both the conviction and the sentence. Torres-Arboledo v. State, 524 So.2d 403 (Fla.), cert. denied, 488 U.S. 901, 109 S.Ct. 250, 102 L.Ed.2d 239 (1988).[1] We affirmed the jury override because the sole factors upon which the jury could have relied in making its recommendation, namely Torres-Arboleda's intelligence and potential for rehabilitation, were not of "such weight that reasonable people could conclude that they outweigh the aggravating factors proven." Id. at 413.
After the Governor issued a death warrant in 1990, Torres-Arboleda filed an "Emergency Motion to Vacate Judgment of Conviction and Sentence" raising fourteen claims. The circuit court granted a stay of execution, ordered an evidentiary hearing as to all claims of ineffective assistance of counsel, and ore tenus summarily denied all other claims. After evidentiary hearing, the circuit court denied relief as to the ineffective assistance of counsel claims as well.
Torres-Arboleda raises the following thirteen claims[2] in the appeal of the denial of his rule 3.850 motion: 1) defense counsel was ineffective at the guilt phase; 2) newly discovered evidence proves his innocence; 3) defense counsel was ineffective at the penalty phase; 4) prosecutorial comments rendered his trial unfair; 5) his absence during the charge conferences and lack of transcription of the conferences denied him due process; 6) the trial court and this Court failed to properly evaluate mitigation evidence; 7) the prosecutor improperly argued nonstatutory aggravating factors; 8) improper victim impact and victim characteristic evidence was considered; 9) felony murder constituted an automatic aggravating circumstance; 10) hearsay statements were improperly introduced during the penalty phase; 11) the trial court relied on an unconstitutional prior conviction as an aggravating circumstance; 12) the cumulative effect of procedural and substantive errors deprived him of fair trial; and 13) the application of Florida Rule of Criminal Procedure 3.851 violated his due process rights.
The majority of these claims are either procedurally barred or without merit. Proceedings under rule 3.850 are not to be used as a second appeal; nor is it appropriate to use a different argument to relitigate the same issue. Medina v. State, 573 So.2d 293, 295 (Fla. 1990). Likewise, issues that could have been raised on direct appeal, but were not, are not cognizable through collateral attack. See Johnson v. State, 593 So.2d 206 (Fla.) cert. denied, ___ U.S. ___, 113 S.Ct. 119, 121 L.Ed.2d 75 (1992); Smith v. State, 445 So.2d 323 (Fla. 1983), cert. denied, 467 U.S. 1220, 104 S.Ct. 2671, 81 L.Ed.2d 375 (1984). Applying this standard to the claims raised by Torres-Arboleda, we find that issues four, five, and seven through twelve are procedurally barred because they should have been raised on direct appeal but were not. To the extent that issue four also raises a claim that the State made an improper "Golden Rule" argument during the guilt phase closing arguments, that claim was previously raised on direct appeal and specifically rejected by this Court. Torres-Arboledo, 524 So.2d at 411. We find no merit to issue six that claims that both the trial court and this Court failed to properly evaluate the mitigation evidence presented. See Torres-Arboledo, 524 So.2d at 413, for discussion of jury override and mitigation evidence presented. We also find issue thirteen to be without merit. To the extent that these issues raise claims of ineffective assistance of counsel, we find no merit as Torres-Arboleda has failed to demonstrate deficient performance or prejudice as required by Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984). Consequently, we deny claims four through thirteen.
Torres-Arboleda also claims that counsel rendered ineffective assistance during both the guilt and penalty phases. Under the two-prong Strickland test, Torres-Aboleda must demonstrate that 1) counsel's performance was deficient and 2) there is a reasonable probability that the outcome of the proceeding would have been different. Id. at 687, 694, 104 S.Ct. at 2064, 2068. A court considering a claim of ineffective counsel need not determine whether counsel's performance was deficient when it is clear that the alleged deficiency was not prejudicial. Kennedy v. State, 547 So.2d 912, 913 (Fla. 1989).
In issue one, Torres-Arboleda argues that counsel was ineffective during the guilt phase for failing to: investigate and present alibi evidence; impeach State witnesses on the number of their prior convictions; urge that State witnesses were biased; and challenge the State's evidence regarding the murder weapon. The record reflects that defense counsel did ask State witnesses Raymond Jacobs, Fernando Munoz, and George Williams about previous convictions. Although the exact number of convictions was not elicited in each instance, each of the witnesses admitted that he had previous convictions. Counsel also elicited that witness Eva Munoz was married to Fernando Munoz and that Fernando was currently serving time in prison. Furthermore, counsel did question Williams about a reduction in his sentence, but Williams denied that the State had made any deal with him. Based upon this record, we do not find that defense counsel was deficient in either impeaching State witnesses or arguing witness bias. Moreover, we do not find that counsel's performance relating to the murder weapon was deficient. Torres-Arboleda claims that counsel should have argued that the gun could have belonged to the victim and that the shooting could have occurred during a struggle for the weapon. However, counsel cannot be faulted for failure to raise these speculations relating to the weapon when defendant steadfastly maintained his alibi defense.
While failure to thoroughly investigate the alibi defense may constitute deficient performance under circumstances of this case, we find that Torres-Arboleda has failed to establish the prejudice prong of the Strickland test. Four of Torres-Arboleda's friends testified that he was in Tampa shortly before or shortly after the shooting of Lorenzo, which is contrary to the alleged alibi testimony offered at the 3.850 evidentiary hearing. Three other witnesses placed Torres-Arboleda at the scene of the homicide. Thus, we cannot say there is a reasonable probability that the outcome of the proceeding would have been different had counsel presented this alibi evidence.
We also reject Torres-Arboleda's alternative claim in issue two that this alibi evidence constituted newly-discovered evidence of innocence which requires reversal of his conviction. Two requirements must be met in order to set aside a conviction or sentence because of newly discovered evidence. First, the asserted facts "must have been unknown by the trial court, by the party, or by counsel at the time of trial, and it must appear that defendant or his counsel could not have known them by the use of diligence." Hallman v. State, 371 So.2d 482, 485 (Fla. 1979), abrogated on other grounds, Jones v. State, 591 So.2d 911 (Fla. 1991). Second, "the newly discovered evidence must be of such nature that it would probably produce an acquittal on retrial." Jones, 591 So.2d at 915. We find that the claim fails to meet both of these requirements. First, the defendant was aware of this alibi evidence at the time of trial and counsel could have known about it through diligent investigation. Second, for the same reasons discussed in issue one, this evidence probably would not produce an acquittal on retrial in the face of contradictory testimony that placed the defendant at the scene of the homicide.
However, we do find merit to Torres-Arboleda's claim in issue three that defense counsel rendered ineffective assistance of counsel during the penalty phase. The original sentencing court found two aggravating circumstances and no mitigating circumstances. The only mitigating evidence that counsel presented during the penalty phase was the expert testimony of clinical psychologist Dr. Mussenden, who testified that Torres-Arboleda was very intelligent and an excellent candidate for rehabilitation. Torres-Arboledo, 524 So.2d at 413. In affirming the sentencing court's override of the jury's recommended life sentence, this Court stated:
It is apparent from the record that Torres-Arboledo's intelligence and potential for rehabilitation were the sole factors upon which the jury could have relied in making its recommendation. We do not believe that these factors, for which the sole support was the testimony of an expert witness, are of such weight that reasonable people could conclude that they outweigh the aggravating factors proven.
Id.
During the 3.850 hearing, collateral counsel presented substantial mitigation evidence that trial counsel could have discovered if he had conducted a reasonable investigation of Torres-Arboleda's background. Documentary evidence showed that Torres-Arboleda had a history of good behavior during his incarceration in California, had no police record in Colombia, and had attended a university in Colombia. These documents should have been considered in mitigation as such factors may show potential for rehabilitation and productivity within the prison system. See Stevens v. State, 552 So.2d 1082, 1086 (Fla. 1989); Holsworth v. State, 522 So.2d 348, 354 (Fla. 1988). Additionally, these documents could have provided independent corroborative data for Dr. Mussenden's opinion that the defendant had a good potential for rehabilitation. Instead, Dr. Mussenden relied upon the defendant's self-report and some psychological tests as the basis for his opinion.
Testimony at the postconviction proceeding also revealed that Torres-Arboleda grew up in abject poverty in Colombia, was a good student and child, and supported his family after his father's death. Such evidence of family background and personal history may be considered in mitigation. Stevens, 552 So.2d at 1086; Brown v. State, 526 So.2d 903, 908 (Fla.), cert. denied, 488 U.S. 944, 109 S.Ct. 371, 102 L.Ed.2d 361 (1988).
Counsel also failed to present evidence during the penalty phase of a contract of immunity between the State and another alleged perpetrator. Because the court had ruled the contract inadmissible on relevancy grounds during the guilt phase, counsel deemed it irrelevant and inadmissible during the penalty phase as well, and thus never sought to introduce it. However, evidence of disparate treatment of a co-perpetrator can serve as a reasonable basis for a jury's recommendation of life. Fuente v. State, 549 So.2d 652, 658 (Fla. 1989); McCampbell v. State, 421 So.2d 1072, 1076 (Fla. 1982).
In fact, the evidence presented at this 3.850 hearing is exactly the type of mitigating factors that this Court found lacking in Torres-Arboleda's case on direct appeal. Torres-Arboledo, 524 So.2d at 413. Torres-Arboleda cited McCampbell to support his direct appeal claim that the jury's life recommendation was reasonable. In response, this Court noted that McCampbell involved four mitigating factors not present in Torres-Arboleda's case, namely "exemplary employment record; prior record as a model prisoner; family background; and the disposition of the codefendants' cases" which "served as reasonable bases for the jury's recommendation of life." Torres-Arboledo, 524 So.2d at 413. Had counsel presented these mitigating factors during the penalty phase, our analysis of the jury override issue could have been quite different.
During testimony at the postconviction proceeding, trial counsel admitted that he had no strategic reason for failing to present this mitigating evidence during the penalty phase. Counsel considered some of the evidence to be irrelevant or inadmissible (police report of no prior criminal history; State's contract of immunity with suspected co-perpetrator) and was unaware that he could obtain other evidence (California prison records). Counsel made no attempt to investigate Torres-Arboleda's family history and background, work history, or school record in Colombia. In fact, he never even made an application to the court for funds to investigate in Colombia because he did not think the court would approve such a request. Notwithstanding counsel's belief that the trial judge would impose a death sentence, he failed to present any mitigating evidence to the jury other than Dr. Mussenden's testimony and testing because "I felt that that's all I had. That's all that I could go with." At sentencing, counsel offered nothing other than legal argument that the jury's recommendation should be given great weight.
Based upon the testimony and documentary evidence presented during the postconviction proceeding, Torres-Arboleda has shown "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 694, 104 S.Ct. at 2068. This mitigating evidence, which existed at time of trial, "might have provided the trial judge with a reasonable basis to uphold the jury's life recommendation." Heiney v. State, 620 So.2d 171, 174 (Fla. 1993). Had these factors been discovered and presented to the court at Torres-Arboleda's original sentencing, there would have been a reasonable basis in the record to support the jury's recommendation and the jury override would have been improper. See Ferry v. State, 507 So.2d 1373, 1376 (Fla. 1987). Thus, counsel's failure to investigate and present mitigating evidence prejudiced Torres-Arboleda.
Accordingly, we find that the 3.850 court erred in determining that counsel was not deficient in failing to investigate and present mitigating evidence during the penalty phase and in finding that Torres-Arboleda was not prejudiced by this failure. Thus, we vacate Torres-Arboleda's sentence of death and remand for a resentencing hearing before the judge. It is unnecessary to conduct the hearing before a jury as Torres-Arboleda is entitled to the benefit of the previous jury's life recommendation. Heiney, 620 So.2d at 174.
It is so ordered.
BARKETT, C.J., and OVERTON, SHAW, KOGAN and HARDING, JJ., concur.
GRIMES, J., concurs in part and dissents in part with an opinion, in which McDONALD, J., concurs.
GRIMES, Justice, concurring in part and dissenting in part.
I cannot agree that if the additional mitigating evidence referred to in the majority opinion had been introduced, the jury override would have probably been reversed. In the first place, there was already evidence before the jury of Torres-Arboleda's education and his prospects for rehabilitation. In view of the aggravating factor of the commission of another murder, the additional evidence of an impoverished childhood would not have made the jury's life recommendation reasonable. The trial judge was aware of the contract of immunity given to the third participant, and in any event, all of the evidence indicated that Torres-Arboleda actually did the killing.
The trial judge conducted a full evidentiary hearing and concluded that any shortcomings of defense counsel would have made no difference. There is ample record support for this ruling, and it should be affirmed.
McDONALD, J., concurs.
NOTES
[1] On direct appeal, this case was styled as Torres-Arboledo v. State based upon the filings in the case. Apparently, the correct spelling of the defendant's name is reflected in the style of the instant case.
[2] Torres-Arboleda also raises ten claims in his habeas petition to this Court. These claims essentially duplicate the claims raised in the rule 3.850 appeal and will not be treated separately in this opinion. To the extent that these habeas claims allege ineffective assistance of appellate counsel, we find that such claims are without merit. Moreover, an allegation of ineffective assistance will not be permitted to serve as a means of circumventing the rule that habeas proceedings do not provide a second or substitute appeal. Blanco v. Wainwright, 507 So.2d 1377, 1384 (Fla. 1987).