How have the courts interpreted the doctrine of "unreasonable self-defense" at the penalty phase?

Defendant contends that the trial court erred when it rejected his proffered instruction on "unreasonable self-defense" or imperfect self-defense pursuant to People v. Flannel (1979) 25 Cal.3d 668. He asserts that the instruction was justified because of statements he made to the police that he fired at the victims in response to gunfire he believed was directed at him. Defendant acknowledges that this doctrine applies to the issue of guilt. (Id. at p. 672 [a defense of imperfect self-defense "negates malice so that the offense is reduced from murder to manslaughter"].) Nonetheless, he maintains that, had the instruction been given at the penalty phase, "defense counsel would have been able to remind [the jury] of this legal principle... and argue that lingering doubt [remained] concerning [defendant's] mistake of fact in determining whether [defendant's] should be sentenced to death."