WASHINGTON — In the summer of 2014, Terrence Byrd was driving a rental car on an interstate highway in Pennsylvania. His fiancée had rented it, and he was using it with her permission. But he was not listed on the rental agreement as an authorized driver.

A state trooper, David Long, noticed Mr. Byrd and decided to follow him. At a hearing months later, Trooper Long testified that Mr. Byrd had aroused his suspicion by holding the steering wheel as driving instructors recommend, at the “10 and 2” position, and by sitting far back in his seat.

A lawyer for Mr. Byrd seemed incredulous about all of this.

“So the only reason you pulled out was the fact that he was at 10 and 2 and you couldn’t see him?” the lawyer asked.

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Trooper Long then mentioned a third factor. “In a rental vehicle,” he said. “That’s what drew my attention to it, yes.”

In short order, Trooper Long pulled Mr. Byrd over, for failing to move into the right lane fast enough after passing a slow-moving truck. At that point, the car rental company’s boilerplate contract collided with the Fourth Amendment, which bars unreasonable searches.

Because Mr. Byrd was not listed as an authorized driver, Trooper Long said he was free to search the car without Mr. Byrd’s consent. He found body armor and 49 bricks of heroin in the trunk.

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

Next week, the Supreme Court will consider whether privacy rights turn on the fine-print contracts signed by the more than 115 million people who rent cars every year. “If the government prevails,” Mr. Byrd’s lawyers wrote in a brief filed last week, “it will have the power to conduct suspicionless searches whenever it stops a rental car driven by an unlisted driver for a routine traffic violation.”

Letting a family member or a friend drive a car you have rented can be a breach of the rental contract. But it is not generally considered a crime, and it is not obvious that people who drive cars that others have rented should forfeit their Fourth Amendment rights.

The contract in Mr. Byrd’s case, from Budget, was typical. It said that “the only ones permitted to drive the vehicle other than the renter 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.”

Mr. Byrd was none of those. 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.

In rejecting Mr. Byrd’s appeal, the United States Court of Appeals for the Third Circuit, in Philadelphia, acknowledged that federal appeals courts have differed about “whether the sole occupant of a rental vehicle has a Fourth Amendment expectation of privacy when that occupant is not named in the rental agreement.” The Third Circuit’s own precedents, the court said, “determined such a person has no expectation of privacy and therefore no standing to challenge a search of the vehicle.”

Mr. Byrd’s lawyers said this ignored reality. “Widespread noncompliance with authorized-driver provisions is an open secret,” they wrote, which is why rental agreements “often specify that the renter will carry greater risk of loss when an unlisted driver operates the vehicle.”

The Supreme Court’s decision in the case, Byrd v. United States, No. 16-1371, is very likely to have an outsize effect on black and Hispanic drivers, according to a brief from the American Civil Liberties Union and the National Association of Criminal Defense Lawyers.

Poor people rent a lot of cars. “There is a commonly held misconception that car rental is a luxury reserved for the wealthiest individuals,” a 2010 tax study found, noting that “more car rentals occur at neighborhood locations than at airport locations.”

“African-Americans generate over four times as many retail rental transactions as otherwise comparable Caucasians,” the study said. Otherreports have demonstrated that black drivers are more likely than white ones to be pulled over by the police and more likely to be searched during the stop.

Solicitor General Noel J. Francisco urged the justices to hold Mr. Byrd to the terms of the rental agreement. “It is common knowledge,” he wrote, “that car rental is a personal transaction that does not make the car available for general enjoyment, and straw man car rentals disserve society by frustrating law-enforcement efforts to prevent smuggling and other crimes.”

In a brief supporting the federal government, 15 states said criminals often used cars rented by others to transport drugs, victims of human trafficking and unauthorized immigrants.

It is certainly true that allowing the police to search rental cars whenever they pull over an unlisted driver would yield evidence of crimes. “But what is expedient for law enforcement is not the test,” Mr. Byrd’s lawyers wrote.

Justice Antonin Scalia, who died in 2016, made a similar point during a 2013 argument over whether the Fourth Amendment allowed the police to take DNA samples from people they arrest. A government lawyer said the practice had led to many convictions.

Justice Scalia was unimpressed.

“Well, that’s really good,” he said, with characteristic sarcasm. “I’ll bet you if you conducted a lot of unreasonable searches and seizures, you’d get more convictions, too. That proves absolutely nothing.”

Follow Adam Liptak on Twitter at @Adamliptak.