This critique first identifies the components of death-penalty due process which emerged from Furman v. Georgia (1972) and subsequent 1976 Court decisions pertaining to State capital punishment schemes. The paper then discusses selected Supreme Court decisions that implemented the 1976 standards, decisions that apparently indicated the Court's resolve to implement these standards. The paper concludes that these decisions deepened the dilemma created by the contradictory themes of the 1976 decisions. The final section of the critique discusses the Court's 1983-84 decisions deemed to have abandoned its previous due process standards in death penalty cases. The author argues that Barefoot v. Estelle (1983) produced two propositions: (1) either capital appellants are to receive no more process than that afforded ordinary litigants; or (2) they are to receive less process because, unlike appeals of prison sentences, the sentence cannot begin while appeals are being pursued. Zant v. Stephens (1983) and Barclay v. Florida (1983) are indicated to abandon the guided discretion for death sentences set in 'Furman.' The author reasons that in Pulley v. Harris (1984), the Court decided that proportionality review is not a constitutional requirement in capital cases. In the context of the Supreme Court decisions reviewed, the paper advises defense attorneys in capital cases to assume that the trial court will be the final forum that determines the defendant's fate. A total of 200 footnotes are listed.