Abolitionists' arguments against the death penalty are cited as follows: it is discriminatorily applied against killers whose victims are white; minorities are excluded from juries, but nearly 50 percent of death row inmates are members of minority groups; and there is risk of executing someone who may later be found innocent. Arguments of death penalty advocates are also presented; for example, they argue that the threat of capital punishment deters crime and that capital punishment expresses the public sentiment that murder will not be tolerated. Evidence that abolitionists are losing ground on many of their defenses is presented; recent decisions by the U.S. Supreme Court and two circuit courts of appeals, for example, have rejected the issue of discrimination based on the race of the victim, and the Supreme Court has also ruled that Federal appeals courts can expedite death penalty appeals. Further, the Supreme Court's 1972 ruling in Furman v. Georgia, i.e., that the death penalty was unconstitutional, is discussed, as is its 1976 ruling in Gregg v. Georgia, which held that death penalty statutes are constitutional if judges and juries use 'guided discretion' in sentencing. Abolitionists' contentions about the arbitrariness of post-Furman laws are noted, and their concession that chances of overturning death penalty laws are remote is reported. Finally, the public's increased support for capital punishment is shown to parallel its get-tough attitude toward crime. Included are 16 photographs and a table showing the number of death row inmates and executions since 1977 as of January 31, 1985, for the States with the death penalty.