The empirical evidence on capital sentencing that does exist suggests that arbitrariness and discrimination still occur, although less severely than during the pre-Furman era. Evidence also indicates that the extent of arbitrariness and discrimination varies considerably among jurisdictions and various stages of the death sentencing selection process. Because State supreme courts lack the data that would document the existence of arbitrariness and discrimination in capital sentencing, they have vacated few post-Furman death sentences as excessive, disproportionate, or discriminatory. Such data have not been collected by State supreme courts probably due to justices' fear that the courts cannot competently collect and analyze such data. This article suggests remedies for excessiveness and discrimination in death sentencing and proposes a method for measuring excessiveness and racial discrimination within a capital sentencing system. 11 tables, 3 figures, 132 footnotes, and appended supplementary information. (Author summary modified)