In Ullmann v. United States, the Supreme Court ruled on a case involving the Fifth Amendment's protection against self-incrimination. The defendant, Louis Ullmann, had been granted immunity from prosecution in exchange for his testimony before a grand jury investigating espionage activities. However, he refused to testify citing his Fifth Amendment rights and was held in contempt of court. In its decision, the Supreme Court upheld that an individual cannot invoke their right against self-incrimination if they have been granted immunity that is coextensive with this constitutional protection - meaning it offers equivalent protections as those guaranteed by the Constitution itself. Therefore, since Ullman’s immunity protected him from being prosecuted based on his testimony or any evidence derived from it (which matches the scope of Fifth Amendment protections), he could not refuse to testify under these circumstances without facing penalties for contempt of court.

In the dissenting opinion for ULLMANN v. UNITED STATES, Justice Douglas argued that the majority's decision to uphold a law compelling testimony in exchange for immunity from prosecution was an infringement on individual liberties protected by the Fifth Amendment. He contended that this ruling allowed prosecutors too much power and discretion over witnesses, potentially leading to abuses of authority and coercion. Furthermore, he expressed concern about how such compelled testimonies could be used against individuals in other legal proceedings or contexts outside of criminal prosecutions - despite supposed protections offered by immunity grants. In essence, Justice Douglas believed that forcing someone to testify under threat of contempt charges violated their constitutional right against self-incrimination even if they were granted immunity from prosecution based on their testimony.