In Boag v. MacDougall, the petitioner, a prisoner on death row in Arizona, argued that his execution by lethal gas violated the Eighth Amendment's prohibition against cruel and unusual punishment. He claimed that this method of execution caused unnecessary physical pain and psychological suffering. The Supreme Court dismissed these claims without comment or explanation, effectively upholding the constitutionality of execution by lethal gas under the Eighth Amendment. This decision was consistent with previous rulings where the court had rejected similar challenges to other methods of capital punishment such as electrocution and hanging.

In the dissenting opinion for Boag v. MacDougall, Justice William Brennan disagreed with the majority's decision to deny certiorari. He argued that there was a significant issue at stake regarding whether or not an individual who is sentenced to death has a constitutional right to have their sentence reviewed by a higher court before it is carried out. Brennan believed that this question deserved serious consideration and examination by the Supreme Court due to its potential implications on capital punishment cases across the country. He also expressed concern about Arizona's unique position as one of only two states in which direct appeal from a death sentence did not automatically stay execution, potentially leading to unjust outcomes if individuals were executed before all appeals processes had been exhausted.