Justice Clarence Thomas dissented, saying the majority had drawn artificial and unworkable distinctions. He was joined by Justice Samuel A. Alito Jr. and, for the most part, by Justice Anthony M. Kennedy.

“If a driver is stopped by a particularly efficient officer,” Justice Thomas wrote, “then he will be entitled to be released from the traffic stop after a shorter period of time than a driver stopped by a less efficient officer. Similarly, if a driver is stopped by an officer with access to technology that can shorten a records check, then he will be entitled to be released from the stop after a shorter period of time than an individual stopped by an officer without access to such technology.”

In a separate dissent, Justice Alito added that much will now turn on the order in which police officers complete their tasks during traffic stops. Issuing a ticket or warning, he said, will now become the last step.

“Most officers will learn the prescribed sequence of events even if they cannot fathom the reason for that requirement,” he wrote. He added, “I would love to be the proverbial fly on the wall when police instructors teach this rule to officers who make traffic stops.”

Justices Thomas and Alito also said that there was no reason to have further proceedings about whether Officer Struble had a reasonable suspicion that justified using Floyd, as they said he had ample reason to be suspicious. There was, they said, an overwhelming odor of air freshener in the vehicle. The reasons Mr. Rodriguez offered for veering onto the shoulder and for his trip were open to question. And the passenger appeared nervous.

“These facts, taken together, easily met our standard for reasonable suspicion,” Justice Thomas wrote.