
514 So.2d 354 (1987)
Amos Lee KING, Jr., Appellant.
v.
STATE of Florida, Appellee.
No. 68631.
Supreme Court of Florida.
September 24, 1987.
Rehearing Denied November 20, 1987.
*355 Baya Harrison, Tallahassee, for appellant.
Robert A. Butterworth, Atty. Gen., and Michael J. Kotler and Robert J. Krauss, Asst. Attys. Gen., Tampa, for appellee.
PER CURIAM.
King appeals his sentence of death imposed on resentencing. We have jurisdiction, article V, section 3(b)(1), Florida Constitution, and affirm the sentence.
While he was an inmate at a work-release correctional facility, the state charged King with the first-degree murder of an elderly woman, the robbery and arson of her home, escape, and the attempted murder of a prison counselor. The jury convicted him as charged and recommended that he be sentenced to death. The trial court imposed a death sentence, and this Court affirmed both the conviction and sentence. King v. State, 390 So.2d 315 (Fla. 1980), cert. denied, 450 U.S. 989, 101 S.Ct. 529, 67 L.Ed.2d 825 (1981).
In 1981 the governor signed a death warrant on King who then filed a motion for postconviction relief, alleging ineffective assistance of trial counsel. After an evidentiary hearing, the trial court denied the motion, and this Court affirmed that denial. King v. State, 407 So.2d 904 (Fla. 1981). King then filed a petition for writ of habeas corpus in federal court, and, on appeal, the eleventh circuit found that King's trial counsel had provided ineffective assistance at the penalty phase of his trial and remanded to the district court for entry of an appropriate writ. King v. Strickland, 714 F.2d 1481 (11th Cir.1983). The United States Supreme Court, however, vacated the eleventh circuit's judgment and remanded for reconsideration in light of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Strickland v. King, 467 U.S. 1211, 104 *356 S.Ct. 2651, 81 L.Ed.2d 358 (1984). On reconsideration the circuit court adhered to its original holding that King's trial counsel rendered ineffective assistance at the penalty phase of King's trial. King v. Strickland, 748 F.2d 1462 (11th Cir.1984), cert. denied, 471 U.S. 1016, 105 S.Ct. 2020, 85 L.Ed.2d 301 (1985).
At the federally mandated resentencing proceeding the trial court empanelled a new jury, both sides presented evidence and argument, and the jury unanimously recommended that King be sentenced to death. The trial court imposed a death sentence, finding five aggravating circumstances (committed while under sentence of imprisonment, previous conviction of violent felony, great risk of death to many persons, committed during burglary and sexual battery, and wicked, evil, atrocious, or cruel) and no mitigating factors. On appeal King claims that the trial court erred by 1) allowing the state to exclude blacks from the jury panel; 2) refusing to allow King to present evidence of his innocence while allowing the state to present evidence of his guilt; 3) refusing to allow presentation of evidence that the death penalty is imposed in a racially discriminatory manner; and 4) allowing the state to present evidence based on hearsay.
The jury pool apparently contained three black prospective jurors. Neither the state nor the defense challenged the first of them, a young black woman, and she eventually sat on the jury. The state did, however, use a peremptory challenge on the second black venireman, a pastor who also drove a school bus. Defense counsel objected to his excusal, citing State v. Neil, 457 So.2d 481 (Fla. 1984). Noting the state's acceptance of the first black prospective juror, the court refused to find excusing the second to be a systematic exclusion and overruled the objection.
Defense counsel also objected to the state's excusing the third black prospective juror, a young woman who worked as a police department clerk-typist, claiming that the state was establishing a pattern of systematically excluding blacks from the jury panel. This woman had initially indicated that she would be unable to follow the law if she were a juror, and the following discussion occurred:
Ms. McKeown [assistant state attorney]: Judge, I still don't believe that we have in any way set any type of systematic exclusion. There is no proof of it. If the Court feels there is, at that juncture we will give a reason for why we are excluding her.
The Court: I think it might be appropriate to give a reason in that the record has something in it. I think it is safe to do that.
Ms. McKeown: Okay. She is a young black female, the Defendant is a young black male. Her response to the Court's inquiry with regard to her feelings about the death penalty we felt were sufficient for us to have concern about how she would apply the law.
Mr. Harrison [defense counsel]: Your Honor, I think that the State has said it better than I could. Miss McKeown wants to excuse this lady in part because of her race, because she is black. She has said that and that is not a Constitutional reason to exclude someone.
* * * * * *
Mr. Sandefer [assistant state attorney]: Miss McKeown and I are working on this together. And we agreed, although we didn't discuss our reasons for it in very much detail to excuse her. My problem that I had with this lady was she originally said she could not follow the law. She then indicated later she could. That caused me some concern. Then she threw up a situation where she said in my reading of the death penalty it is not appropriate for somebody who killed one person. That caused me concern.
Apparently she feels like there has to be past murders involved. Obviously we don't have that. I have concern over her being able to follow the law because of the changes in what she said and the final statement about the death penalty.
The Court: ... She is indicating the law is not evenly followed in all cases.
Mr. Sandefer: That is correct, and that is our concern.

*357 The Court: She said that.
Ms. McKeown: Judge, I would be less than candid if I didn't state the other  I plan on being honest with the Court. I think it is whether or not the sole basis for exclusion is race, and that is certainly not the sole basis for excluding that lady. And, as I think the Court recognizes, we have accepted, do intend to plan on accepting Mrs. McBride who is another young black female on that jury.
Mr. Harrison: Well, Your Honor, I think we have made our position clear. I think that the State has failed the Neal versus State [sic] test. They want to exclude a person because of their race, at least in part, and I think what Sandefer is doing is coming up with excuses to try to reinforce.
The Court: I'll make a ruling. I think her statement with regard to uneven imposing of the death penalty is certainly more than sufficient justification for excusing her. Overrule the objection.
In State v. Neil, 457 So.2d 481 (Fla. 1984), this Court held that peremptory challenges cannot be exercised solely on the basis of race. To challenge the other side's peremptory excusals, a party must object in a timely manner and demonstrate on the record both that those persons challenged are members of a distinct racial group and that there is a strong likelihood they are being challenged solely because of their race. Id. at 486. King has met the first two parts of the Neil test but not the third, i.e., a strong likelihood of being challenged solely because of race. As the above-quoted portion of the record shows the state had several reasons for excusing this prospective juror. The trial judge listened to and questioned this woman, listened to counsels' argument, and evaluated the credibility of all concerned on this issue. We see no reason to disturb his ruling on excusing this prospective juror or his ruling that no systematic exclusion had occurred when the state previously excused the second black prospective juror. See Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 1724 n. 21, 90 L.Ed.2d 69 (1986); Neil, 457 So.2d at 487, n. 10.
King also claims that the trial court erred in allowing the state to present evidence that he committed this murder and in refusing to let him introduce evidence showing his innocence because the federal court "virtually mandated" the introduction of evidence which would have created "lingering doubt" about his guilt. King's current attorney wanted to present an FBI agent's testimony on hair and fiber analysis, wanted to show that the knife admitted into evidence was inconsistent with the victim's wounds, and wanted to attack the circumstantial evidence against King, among other things. At a pretrial consideration of King's motion to present exculpatory evidence King's counsel stated that he disagreed with the eleventh circuit's assessment of King's prior counsel's effectiveness during the guilt portion of King's trial. He said that he "sincerely felt that that question [guilt/innocence] had never been completely resolved" and that he wanted to create in the minds of the jurors a "serious, serious question, serious doubt, a lingering doubt if you will, some doubt of his guilt." The trial court stated that guilt or innocence had been put to rest on appeal and that the current proceeding dealt only with the penalty to be imposed. The state argued that King could testify and deny his guilt, but that he should not be allowed to relitigate his guilt. The court ruled that the question of guilt could not be relitigated, that the proffered evidence was irrelevant to the appropriate penalty, and that the presentation of evidence would be limited to evidence going to aggravating and mitigating circumstances.
We find no error on this point. The state had several witnesses testify as to the circumstances of the crimes and the injuries to the victims. Defense counsel objected numerous times, chiefly to the relevancy of the testimony to the sentencing proceeding, but the court found the state's evidence relevant to showing the existence of statutory aggravating factors. The admissibility of evidence is within the trial court's discretion, and a reviewing court will not disturb a trial court's ruling unless an abuse of discretion is shown. Jent v. *358 State, 408 So.2d 1024 (Fla. 1981), cert. denied, 457 U.S. 1111, 102 S.Ct. 2916, 73 L.Ed.2d 1322 (1982). King has shown no abuse of discretion regarding the court's ruling on the state's evidence. King had been convicted, and his convictions had been affirmed on appeal; his guilt, therefore, was not at issue. The state, however, still needed to prove beyond a reasonable doubt the aggravating circumstances it felt supported a death sentence and, to this end, could present evidence rather than relying on the bare admission of the convictions. See Teffeteller v. State, 495 So.2d 744 (Fla. 1986); Trawick v. State, 473 So.2d 1235 (Fla. 1985), cert. denied, ___ U.S. ___, 106 S.Ct. 2254, 90 L.Ed.2d 699 (1986); Elledge v. State, 408 So.2d 1021 (Fla. 1981), cert. denied, 459 U.S. 981, 103 S.Ct. 316, 74 L.Ed.2d 293 (1982); Thompson v. State, 389 So.2d 197 (Fla. 1980); Elledge v. State, 346 So.2d 998 (Fla. 1977).
The eleventh circuit stated that
King was convicted on circumstantial evidence which however strong leaves room for doubt that a skilled attorney might raise to a sufficient level that, though not enough to defeat conviction, might convince a jury and a court that the ultimate penalty should not be exacted, lest a mistake may have been made.
748 F.2d at 1464. King cites this quote as support for his claim that he should have been allowed to introduce exculpatory evidence. The federal court made that statement to explain the differences between King's case and another case. In reality, however, this statement is only a subsidiary explanation for the court's holding:
King's attorney's failure to present available character witnesses in mitigation and his weak closing argument constituted both an unreasonable professional performance by the attorney and impermissible prejudice to King, thereby denying him effective assistance of counsel at the penalty stage of his trial.
Id. at 1463-64.
In his federal habeas petition King attacked his trial counsel's failure to present the evidence he now complains about. The eleventh circuit specifically found counsel not to be ineffective during the guilt phase of the trial, 714 F.2d at 1488-90, but ineffective at the penalty phase. Id. at 1491; 748 F.2d at 1464. Current counsel disagreed with the eleventh circuit's assessment of original counsel's performance at the guilt phase and attempted to bring exculpatory evidence before the jury on the theory that it would create lingering or whimsical doubt of King's guilt which should be considered as a nonstatutory mitigating circumstance.[1]
The lingering doubt theory has been used several times. Smith v. Wainwright, 741 F.2d 1248 (11th Cir.1984), cert. denied, 470 U.S. 1087, 105 S.Ct. 1853, 85 L.Ed.2d 150 (1985); Smith v. Balkcom, 660 F.2d 573 (5th Cir.1981), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982). This Court, however, has consistently held that residual, or lingering, doubt is not an appropriate nonstatutory mitigating circumstance. Aldridge v. State, 503 So.2d 1257 (Fla. 1987); Burr v. State, 466 So.2d 1051 (Fla.), cert. denied, 474 U.S. 879, 106 S.Ct. 201, 88 L.Ed.2d 170 (1985); Buford v. State, 403 So.2d 943 (Fla. 1981), cert. denied, 454 U.S. 1163, 102 S.Ct. 1037, 71 L.Ed.2d 319 (1982). The only limitation on introducing mitigating evidence is that it be relevant to the problem at hand, i.e., that it go to determining the appropriate punishment. As the trial court did, we find the exculpatory evidence sought to be introduced irrelevant to King's sentence. King has not demonstrated an abuse of discretion, and we will not disturb the trial court's ruling.
In McCleskey v. Kemp, ___ U.S. ___, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987), the United States Supreme Court held statistical studies insufficient to demonstrate unconstitutional discrimination in imposing the death penalty. We therefore find no merit to King's claim that the trial court *359 erred in refusing to allow him to present evidence on such a claim.
Subsection 921.141(1), Florida Statutes (1985), states, in part, that in a capital penalty proceeding the parties may present any evidence "which the court deems to have probative value ... regardless of its admissibility under the exclusionary rules of evidence, provided the defendant is accorded a fair opportunity to rebut any hearsay statements." King now claims that the trial court erred in allowing the state to present hearsay evidence which he could not fairly refute. Specifically, King claims that the testimony of a detective for the state included unsubstantiated hearsay as to 1) the murder victim's awareness of someone trying to break into her home; 2) the broken knitting dowels in the yard being from her home; and 3) the knife found between the work-release center and the victim's home being from her home.
The state asked this detective if the victim might have been aware that someone tried to enter her home. The detective answered "absolutely" and then went on to name the firefighter who had difficulty opening a door to the house because a chair had been propped against the door knob as if to prevent the door from being opened from the outside. Notwithstanding the defense's knowledge of the firefighter's name and that he could have been deposed, our review of the record shows no objection to this item of testimony. Any error, therefore, has been waived.
As to the knitting dowels, the detective stated that a friend of the victim identified them as belonging to the victim. Defense counsel objected on the basis of hearsay and stated that he did not know who the friend was. The assistant state attorney said she could have the witness give the friend's name and that, because that person had been included on the witness list, she could have been deposed by the defense. Counsel, however, stated that the state did not want him to take depositions because the witnesses had been deposed before King's trial.[2] The court responded that if counsel had a complaint it would have been ruled on if brought to the court's attention. The court then held that the issues could not be explored at length and that the relevancy of the testimony outweighed any prejudicial effect. King could, in fact, have rebutted this testimony if he chose to do so, and we find no reversible error in the trial court's ruling.
In response to the state's question if he had determined where the knife came from the detective said that it came from the victim's residence. Counsel objected to introduction of the knife as being irrelevant and also objected both that the state was getting into the guilt-innocence issue[3] and to the hearsay nature of the testimony in regards to guilt-innocence. Counsel did not object to the detective's saying that the knife came from the victim's residence. This statement was not hearsay because no other person ever said the same thing. It may have been a misstatement of the facts, but the medical examiner testified that the knife in evidence was consistent with the murder victim's wounds, the attempted murder victim testified that the knife was similar to the one used on him, and, in closing argument, the state acknowledged that the medical examiner could not positively identify the knife in evidence as the murder weapon.
After examining this record, we do not find that King was denied a fair opportunity to rebut any hearsay. We therefore find no merit to this point on appeal.
King presented several family members, friends, and people involved with prison ministries who testified as to King's childhood, his life in general, and his conduct while in prison. As noted before, however, *360 the jury unanimously recommended that he be sentenced to death which the trial court did, finding five aggravating circumstances and nothing in mitigation. Our review of this record shows ample support for the trial court's findings except for finding that King knowingly created a great risk of death to many persons by setting fire to the murder victim's house.
On his original appeal this Court affirmed the trial court's finding this aggravating factor and stated that "when the appellant intentionally set fire to the house, he should have reasonably foreseen that the blaze would pose a great risk to the neighbors, as well as the firefighters and the police who responded to the call." 390 So.2d at 320. Upon reconsideration we find that this aggravating factor should be invalidated. In Kampff v. State, 371 So.2d 1007, 1009 (Fla. 1979), we stated: "`Great risk' means not a mere possibility, but a likelihood or high probability." Furthermore, we have also said that "a person may not be condemned for what might have occurred." White v. State, 403 So.2d 331, 337 (Fla. 1981), cert. denied, 463 U.S. 1229, 103 S.Ct. 3571, 77 L.Ed.2d 1412 (1983). Only the victim was in the house when King set it on fire. That two firefighters suffered smoke inhalation and that the fire caused considerable damage to the house does not justify finding that this aggravating factor has been established. This case is a far cry from one where this factor could properly be found. E.g., Welty v. State, 402 So.2d 1159 (Fla. 1981) (setting fire to condominium when six elderly people were asleep in other units qualified as great risk of death to many persons).
After striking this factor, however, we are left with four valid aggravating circumstances and no mitigating circumstances. We therefore affirm King's sentence of death.
It is so ordered.
McDONALD, C.J., and OVERTON, EHRLICH, SHAW and GRIMES, JJ., concur.
BARKETT, J., concurs in part and dissents in part with an opinion, in which KOGAN, J., concurs.
BARKETT, Justice, concurring in part, dissenting in part.
While I agree with all other portions of the majority opinion, I must dissent from its conclusion on the issue of lingering-doubt evidence. The decision in Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), in my opinion, casts grave constitutional doubt upon the majority's statement that lingering-doubt evidence is "irrelevant to King's sentence." Lockett announced that a capital sentencer may not be precluded from considering in mitigation
any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death ... . The need for treating each defendant in a capital case with that degree of respect due the uniqueness of the individual is far more important than in noncapital cases.
438 U.S. at 604-05, 98 S.Ct. 2964-65 (emphasis added, footnote omitted). Thus, the lingering-doubt evidence in question here  concerned as it is with "the circumstances of the offense"  constitutes relevant mitigating evidence.
This view is consistent with Smith v. Wainwright, 741 F.2d 1248 (11th Cir.1984), cert. denied, 470 U.S. 1087, 105 S.Ct. 1853, 85 L.Ed.2d 150 (1985), in which the Eleventh Circuit reviewed an ineffective assistance of counsel claim based upon trial counsel's failure to impeach the state's key witnesses with their prior inconsistent statements. The court noted that the failure of counsel to use the statements not only may have affected the outcome of the guilt phase of the trial, but because "jurors may well vote against the imposition of the death penalty due to the existence of `whimsical doubt,'" id. at 1255, may have changed the outcome of the penalty phase:
In this case, use of Wesley and Patricia Johnson's prior inconsistent statements might have created a whimsical doubt that would discourage the court and advisory *361 jury from recommending the death penalty.
Id.
Unable to reach a conclusion concerning counsel's ineffectiveness without an evidentiary hearing to determine whether failure to use the statements was for a valid strategic purpose, the court remanded to the district court to give the state an opportunity to show that "trial counsel's failure to utilize the Johnsons' statements at either the guilt/innocence or penalty phases of the trial was prompted by reasonable trial strategy." Id. at 1256 (emphasis added).
I believe Smith supports the proposition that in certain cases trial counsel's failure to introduce lingering-doubt at the penalty phase may constitute ineffectiveness. In light of this, I believe it is wrong for this Court to endorse the exclusion of this evidence from the penalty phase.
As the majority notes, the Eleventh Circuit found that:
King was convicted on circumstantial evidence which however strong leaves room for doubt that a skilled attorney might raise to a sufficient level that, though not enough to defeat conviction, might convince a jury and a court that the ultimate penalty should not be exacted, lest a mistake may have been made.
King v. Strickland, 748 F.2d 1462, 1464 (11th Cir.1984), cert. denied, 471 U.S. 1016, 105 S.Ct. 2020, 85 L.Ed.2d 301 (1985).
The defendant should not lose the advantage of this argument merely because a new jury has been impaneled.
KOGAN, J., concurs.
NOTES
[1]  Lingering doubt is what the eleventh circuit must have meant in its discussion of why King's original trial counsel rendered ineffective assistance by failing to present witnesses and argue more persuasively.
[2]  Despite the state's opposition, defense counsel deposed the medical examiner. Presumably, he could have deposed other persons named on the witness list as well.
[3]  In this argument King is again claiming that he needed an expert appointed so that he could challenge the state's evidence used against him at trial, most specifically the knife which the state claimed King used on both of the victims. Again, we find no error in trial court's refusal to allow King to present evidence of his innocence.
