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(2003).” Nor is defendant required to “establish ‘a nexus’” between the mitigation evidence and the crime. Height v. State, 278 Ga. 592, 604 S.E.2d 796 (November 8, 2004). “Georgia’s general ban on the admission of polygraph test results absent the parties’ stipulation should not be applied automatically in the sentencing phase of a capital case so as to prevent the defendant from presenting a favorable polygraph test result. ‘[E]videntiary rules may be trumped by a defendant’s need to introduce mitigation evidence. [Cits.]’ Barnes v. State, [269 Ga. 345, 358(27), 496 S.E.2d 674 (1998)]. Therefore, to the extent that Baxter v. Kemp, 260 Ga. 184, 187(8), 391 S.E.2d 754, fn. 4 (260 Ga. 184, 391 S.E.2d 754) (1990) or any other case intimates that unstipulated polygraph results are per se inadmissible as mitigation evidence, it is hereby overruled. We caution, however, that today’s holding should not be misconstrued as authorizing the admission of polygraph test results in the penalty phase of every capital case. While the scope of permissible mitigation evidence is wide, it is not so extensive as to allow ‘the wholesale admission of all evidence contended to be mitigating without respect to its reliability ...’ Gissendaner v. State, 272 Ga. 704, 714(12), 532 S.E.2d 677 (2000). When the defendant seeks to introduce unstipulated polygraph test results as mitigation evidence, the trial court must exercise its discretion to determine whether those results are sufficiently reliable to be admitted. [Cit.]” Tennard v. Dretke, 542 U.S. 274, 124 S.Ct. 2562, 159 L.Ed.2d 384 (June 24, 2004). “ McKoy v. North Carolina, 494 U.S. 433, 440-441, 110 S.Ct. 1227, 108 L.Ed.2d 369 (1990), … established that the ‘meaning of relevance is no different in the context of mitigating evidence introduced in a capital sentencing proceeding’ than in any other context, and thus the general evidentiary standard — ‘“‘any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence’”’ – applies. Id., at 440, 110 S.Ct. 1227 (quoting New Jersey v. T.L. O., 469 U.S. 325, 345, 105 S.Ct. 733, 83 L.Ed.2d 720 (1985)). … ‘[V]irtually no limits are placed on the relevant mitigating evidence a capital defendant may introduce concerning his own circumstances’ [Cit.].” “[I]mpaired intellectual functioning is inherently mitigating: ‘[T]oday our society views mentally retarded offenders as categorically less culpable than the average criminal,’” Atkins v. Virginia , 536 U.S. 304, 316, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). Defendant was entitled to a certificate of appealability on whether trial court’s jury instruction prevented jury from considering his low IQ score as a mitigating factor. Based on Penry v. Lynaugh , 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989) (“[I]t is not enough simply to allow the defendant to present mitigating evidence to the sentencer. The sentencer must also be able to consider and give effect to that evidence in imposing sentence.”), and Penry v. Johnson , 532 U.S. 782, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001). Three dissent. Head v. Thomason, 276 Ga. 434, 578 S.E.2d 426 (March 24, 2003). “We conclude, given the importance of mitigating evidence in death penalty cases, that an attorney has not acted reasonably when he fails to call mental health experts he knows have mitigating evidence and explains his failure to present lay mitigating evidence by asserting that he had no experts to call.” Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (April 18, 2000). Defendant received ineffective assistance of counsel in his death penalty sentencing phase: “the failure to introduce the comparatively voluminous amount of evidence that did speak in Williams’ favor was not justified by a tactical decision to focus on Williams’ voluntary confession. Whether or not those omissions were sufficiently prejudicial to have affected the outcome of sentencing, they clearly demonstrate that trial counsel did not fulfill their obligation to conduct a thorough investigation of the defendant’s background. See 1 ABA Standards for Criminal Justice 4-4.1, commentary, p. 4-55 (2 nd ed., 1980).” Terrell v. State, 271 Ga. 783, 523 S.E.2d 294 (November 1, 1999). At sentencing phase of defendant’s capital murder trial, trial court properly excluded defendant’s proffered evidence. “In an attempt to cause the jury to have ‘residual doubt,’ he sought to introduce evidence that he offered to plead guilty to the forgeries in exchange for consecutive sentences totaling 100 years, but that he refused to plead guilty to murder. While the permissible scope of mitigation evidence is wide, Barnes v. State, 269 Ga. 345(27), 496 S.E.2d 674 (1998), the trial court correctly refused to admit this evidence. For policy reasons, evidence of a defendant's conditional offer to plead guilty is not admissible in the sentencing phase. Mobley v. State, 265 Ga. 292(18), 455 S.E.2d 61 (1995).” Speed v. State, 270 Ga. 688, 512 S.E.2d 896 (March 1, 1999). At sentencing phase of defendant’s death penalty trial for murder of a police officer, trial court properly ruled out evidence of “police treatment of other young black males” in the area. “While the permissible scope of mitigation evidence is wide, mitigation evidence must relate to the defendant’s character or background or circumstances of the offense on trial. Barnes [ v. State, 269 Ga. 345, 359-60(27), 496 S.E.2d 674 (1998)].”