Decided December 9, 1975
Mosley was arrested by a Detroit PD detective who was investigating a couple of robberies. He given a Miranda advisement and he initially waived his rights, but after a few questions he said that he didn't want to talk about the robberies (he did not ask for a lawyer, he just said that he didn't want to talk about the robberies). The interrogation was promptly terminated.
A couple hours later, a homicide detective interrogated Mosley about a murder. The murder was entirely unrelated to the robberies, and the interrogation took place in a different location than the robbery interrogation had taken place. Prior to the interrogation, Mosley was again advised of his Miranda rights (which he again waived). Mosley made some incriminating statements, and was eventually convicted of murder. He appealed his conviction, arguing that his statements should have been suppressed under Miranda.
The US Supreme Court discussed the irrational extremes that would be possible under Miranda. On one hand, it Miranda could be applied so that once a suspect has invoked his right to remain silent, the police may never again custodially interrogate him for any reason, about any case, at any time in the future. And any statement made after the invocation of rights could be held to be a per-se violation of Miranda, even if the suspect knowingly and voluntarily waived his rights and made a statement. On the opposite extreme, Miranda could be held to require that if a suspect invokes his rights then the police need only stop questioning for a moment, and then they may resume the very same interrogation. I'm not making any of this up, it's all discussed in the decision.
Obviously the Court didn't agree with any of the above possibilities. They held that the critical safeguard of Miranda is a suspect's right to "cut off questioning," and so the test for the admissibility of post-advisement statements is whether that right was scrupulously honored. The court also contrasted this case with a previous case from 1966 (Westover v. U.S.). In Westover, a suspect was interrogated for a couple hours by state LEOs without being advised of his rights. Then the feds took over, read him his rights, and he confessed. The court at that time held that the interrogation by federal officials benefited from the pressures of the previous illegal interrogation, and that the advisement was too little, too late. You can't interrogate someone, then read them Miranda, then use a subsequent waiver to rehabilitate (or continue) the earlier interrogation.
This case was not like that one; in this case, the US Supreme Court held that the Detroit PD scrupulously honored Mosley's request to cut off questioning. They didn't refuse to end the first interrogation and they didn't use repeated requested for new interrogations to wear down his resistance. They immediately ceased interrogation when he invoked his rights, and the second interrogation happened after a significant passage of time and a renewed Miranda waiver, and was limited to a crime entirely unrelated to the first interrogation. For these reasons, the Supreme Court held that Mosley's incriminating statements were admissible.