WASHINGTON >> The Supreme Court today seemed inclined to rule that people not listed as authorized drivers on rental car agreements nonetheless have privacy rights when they are pulled over by the police.

Violating a rental agreement by letting a family member or friend drive a car may be a breach of a commercial contract, several justices said. But it does not follow, they added, that the police may search the cars without the driver’s consent.

The alternative, Justice Sonia Sotomayor said, would give the police too much power.

“If we rule that someone without permission has no expectation of privacy even when the renter has given it to them,” she said, “then what we’re authorizing is the police to stop every rental car and search every rental car, without probable cause, that might be on the road.”

Several justices said that violating other provisions of a rental contract — by talking on a cellphone, say, or driving on an unpaved road — should not lead to the forfeiture of constitutional protections. They suggested that failing to list an additional driver was, similarly, a mere breach of contract that does not overcome the protections of the Fourth Amendment, which bars unreasonable searches.

The case started in 2014, when Terrence Byrd was pulled over by a state trooper on an interstate highway in Pennsylvania. His fiancée had rented the car, from Budget, and he was using it with her permission. But he was not listed on the rental agreement as an authorized driver.

“The only ones permitted to drive the vehicle other than the renter,” the Budget contract said, “are the renter’s spouse, the renter’s co-employee (with the renter’s permission, on company business) or a person who appears at the time of the rental and signs an additional driver form.”

Byrd did not qualify. But he testified that he and the woman who rented the car, Latasha Reed, had been together for 17 years, had five children and were engaged to be married.

On learning that Byrd was not an authorized driver, the trooper maintained that he was free to search the car without Byrd’s consent. He found 49 bricks of heroin in the trunk.

After a judge refused to suppress the evidence, Byrd was convicted of federal drug charges and sentenced to 10 years in prison.

There is nothing particularly unusual about letting others drive rental cars, some justices said. “This is probably not the only time it’s ever happened,” Chief Justice John G. Roberts Jr. said dryly, to laughter.

But Justice Anthony M. Kennedy said that Byrd was not an ordinary unauthorized driver, saying that he had consciously chosen not to be listed.

“The case is presented as if the car was just lent to him for a few minutes,” Kennedy said of Byrd. “What happened was he waited right outside the rental car place while she went in and signed the agreement. It was very clear that he didn’t want to be on the car rental and it was very clear that he was going to be the only one to drive it.”

Eric J. Feigin, a lawyer for the federal government, said Byrd was in no position to assert Fourth Amendment rights.

“As an unauthorized driver, he doesn’t have any connection to the car at all,” Feigin said. “He is not part of the rental agreement. He is an interloper in the rental agreement.”

The justices asked more than the usual number of hypothetical questions during the argument of the case, Byrd v. United States, No. 16-1371.

“What if the Budget rental agreement had, you know, in big letters on it, ‘If anyone is stopped driving this car, they must consent to police search’?” Roberts asked.

Robert M. Loeb, a lawyer for Byrd, said “those provisions would not define what a person’s constitutional rights are.”

The chief justice did not seem satisfied. “It’s their car,” he said, referring to the rental company. “They want to cooperate with the police in terms of what can be used in their car.”

Justice Samuel A. Alito Jr. asked whether Budget could have said in its contract “that if any unauthorized person uses the car, we consent to a search by the police.”

Loeb said that was a closer issue. “If they had called Budget and Budget had said as owner we authorize the search,” he said, “it may be that they could have searched the car.”

Justice Stephen G. Breyer said the Supreme Court should try to give clear guidance to lower courts and to the police. “Fourth Amendment law is too complicated in a sense already,” he said.

Breyer then proposed a standard, saying it was simple and easy to use. Unless the driver of a rental car has stolen it or is committing a crime by driving it, he said, the protections of the Fourth Amendment should apply.

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