In the case of Texas v. McCullough in 1985, the U.S Supreme Court ruled that a state could not prosecute an individual for murder after he had already been acquitted by a court-martial on similar charges. The defendant, John McCullough, was accused of killing another serviceman while both were stationed at Fort Bliss military base in El Paso, Texas. He was tried and acquitted by a military court but later indicted on murder charges by the State of Texas based on new evidence. However, citing double jeopardy protections under the Fifth Amendment to the U.S Constitution which prevents an individual from being prosecuted twice for substantially same crime or offense following acquittal or conviction; Justice Thurgood Marshall delivered opinion stating that "the Double Jeopardy Clause bars any subsequent prosecution" if one sovereign entity (in this case: federal government) has already prosecuted and resolved it.

In the dissenting opinion for Texas v. McCullough, Justice Brennan disagreed with the majority's decision to uphold a death sentence despite potential jury bias. He argued that the court should have considered whether or not jurors who were opposed to capital punishment had been improperly excluded from serving on the jury during McCullough's trial. The exclusion of such jurors could potentially violate a defendant’s Sixth Amendment right to an impartial jury and Fourteenth Amendment due process rights, thereby undermining confidence in the fairness of criminal proceedings and sentencing outcomes. Furthermore, he criticized how lower courts handled this issue without properly considering its constitutional implications before reaching their decisions.