In Loving v. United States, 517 U.S. 748, 755, 135 L. Ed. 2d 36, 116 S. Ct. 1737 (1996), the Court further explained this Eighth Amendment narrowing requirement: The Eighth Amendment requires, among other things, that "a capital sentencing scheme must 'genuinely narrow the class of persons eligible for the death penalty and must reasonably justify the imposition of a more severe sentence on the defendant compared to others found guilty of murder.' " Lowenfield v. Phelps, 484 U.S. 231, 98 L. Ed. 2d 568, 108 S. Ct. 546 (1988) (quoting Zant v. Stephens, 462 U.S. 862, 877, 77 L. Ed. 2d 235, 103 S. Ct. 2733 (1983)). Some schemes accomplish that narrowing by requiring that the sentencer find at least one aggravating circumstance. 484 U.S., at 244, 108 S. Ct. , at 554. The narrowing may also be achieved, however, in the definition of the capital offense, in which circumstance the requirement that the sentencer "find the existence of an aggravating circumstance in addition is no part of the constitutionally required narrowing process." Id., at 246. 517 U.S. at 755.