ASHINGTON, June 28 - The Supreme Court on Monday rejected a police interrogation tactic designed to induce suspects to give incriminating statements after purposely delaying Miranda warnings.

The tactic, taught in police training courses, has been growing in popularity, and the Supreme Court decision, a murder case from Missouri, was consequently eagerly awaited by both prosecutors and defense lawyers.

The 5-to-4 vote against the strategy, in an opinion by Justice David H. Souter, was apparently the product of a prolonged struggle inside the court. This case and another Miranda case announced Monday, the second by a 5-to-4 vote in favor of the prosecution, were argued Dec. 9 and were the oldest undecided cases on the docket. In neither case did the five justices in the majority fully agree on a single rationale.

Under the tactic the court invalidated in the Missouri case, the police first question a suspect while withholding the advice required by the Miranda decision of the right to remain silent and to consult a lawyer before answering questions. In not giving the warnings, the police know that any incriminating statements elicited in this phase of the questioning will be inadmissible in court.

The officers then give the suspect a short break before resuming the interrogation, this time with the warnings. Typically, suspects will waive their Miranda rights and then repeat what they had said earlier, prompted by the officers' leading questions and by the sense that it is now too late to turn back.

The issue for the Supreme Court on Monday was whether the answers from that second phase of questioning could be used in court, and the majority's answer was no. Justice Souter said the facts of this case "by any objective measure reveal a police strategy adapted to undermine the Miranda warnings." He said the police had created a situation for the defendant, a woman suspected of murder, "in which it would have been unnatural to refuse to repeat at the second stage what had been said before."

The case, Missouri v. Seibert, No. 02-1371, was a variant of a case the court decided in 1985 called Oregon v. Elstad. In that case, the police went to a young suspect's house to tell his mother that they were arresting him on a burglary charge. Without receiving any Miranda warnings, the suspect gave an incriminating statement. He was then taken to the police station, received the warnings, and gave a full confession. In deciding that the evidence was admissible, the court treated the initial failure to give the warnings as inadvertent rather than strategic, based on confusion about whether the suspect was formally in custody at the time.

Justice Souter said Monday that it "disfigures that case" to regard the Oregon v. Elstad precedent as dictating the admissibility of the statements in the Missouri case. He also noted that four years ago, in Dickerson v. United States, the court rejected a challenge to the Miranda decision itself. Now, he said, "strategists dedicated to draining the substance out of Miranda cannot accomplish by training instructions what Dickerson held Congress could not do by statute."

The defendant in the Missouri case, Patrice Seibert, was interrogated after a fire in her family's mobile home killed a young man who was staying there and caring for her disabled son. Both before and after receiving Miranda warnings, Ms. Seibert admitted her role in setting the fire. The Missouri trial court suppressed the first admissions but allowed the prosecution to introduce the statements she made after receiving the warnings. Ms. Seibert was convicted of murder. The Missouri Supreme Court overturned the conviction, and the state appealed.

Justice Souter's opinion was joined by Justices John Paul Stevens, Ruth Bader Ginsburg and Stephen G. Breyer. Justice Anthony M. Kennedy wrote separately in agreement with the result, proposing a test under which fewer statements would be likely to be excluded than under the majority's approach.

In a dissenting opinion, Justice Sandra Day O'Connor said the court's decision "devours Oregon v. Elstad," a precedent she described as requiring the opposite result. Justice O'Connor said the subjective intent of the officers should make no difference, because a suspect could not know what was in an officer's mind.

Rather, she said, the test should be the voluntariness of the second statements. If the statements were voluntary, they should be admitted, she said, while if involuntary, they should be kept out of court even if the Miranda warnings were given. Chief Justice William H. Rehnquist and Justices Antonin Scalia and Clarence Thomas joined the dissent.

The lineup in the second Miranda case was the same with the exception of Justice Kennedy, who voted on the prosecution side. The question in United States v. Patane, No. 02-1183, was whether physical evidence, a gun in this case, found as the result of statements obtained without Miranda warnings, could be admitted in court. The court's answer was yes.

Federal firearms agents went to Samuel F. Patane's home in Colorado Springs to question him about a report that he had a gun. Before the agents could finish reading Mr. Patane his Miranda rights, he interrupted them, saying that he knew his rights. He then directed them to the gun in his bedroom.

Interpreting the Oregon v. Elstad precedent, the federal appeals court in Denver said the gun could not be introduced as evidence. The Supreme Court overturned that ruling. Justice Thomas, writing for himself, the chief justice and Justice Scalia, said the Miranda rule could not be violated unless statements were actually introduced in court.

Writing separately, Justices Kennedy and O'Connor said there was no need to reach that sweeping conclusion about the underlying meaning of Miranda in order to conclude under the Elstad precedent that the gun was admissible. Justices Souter, Stevens, Ginsburg and Breyer dissented.