Imagine a police officer pulls over a car for a routine traffic violation, such as speeding or driving with a broken taillight. During the stop, the officer develops a hunch that there may be drugs in the car. He contacts a local K-9 unit and requests a trained drug-sniffing dog; when the unit arrives, another officer will walk the dog around the car to see if it alerts to drugs inside. Although the Supreme Court has held that the use of the dog is not a search, the length of a warrantless stop must be reasonable. The officer can’t delay the driver forever.

This raises a question of Fourth Amendment law that has led to a lot of lower court litigation: If the officer has no reasonable suspicion that drugs are in the car — that is, he only has a hunch — how long can the traffic stop be delayed before the dog arrives and checks out the car?

This might seem like a really technical question. But it’s actually pretty important. If courts say that the police can’t extend the stop even one second to bring over the dogs, then the dogs will only be used when they happen to be right there or some reasonable suspicion exists specifically justifying their use. On the other hand, if the courts say that the police can extend the stop for a long time, then the police will be free to bring out the dogs at routine traffic stops whenever they like.

Lower courts have generally answered the question by adopting a de minimis doctrine. Officers can extend the stop and wait for the dogs for a de minimis amount of time. But exactly how long is that?

Just yesterday, the U.S. Court of Appeals for the Eighth Circuit held in United States v. Rodriguez that seven to eight minutes is de minimis. On the other hand, the Supreme Court of Nevada held a few months ago in State v. Beckman that nine minutes is too long.

These are just lower-court decisions, of course, and there is room to argue that duration alone isn’t the only criteria for whether a stop was too long.

Plus, the Supreme Court has been reluctant to announce arbitrary-sounding time limits on Fourth Amendment searches and seizures. Off the top of my head, the only time it has suggested such limits is County of Riverside v. McLaughlin, and even then it did so only because an earlier decision that did not suggest a specific time limit had caused significant chaos in the lower courts in that specific context.

But as of yesterday, the simple (if simplistic) answer to the question might have unusual mathematical precision, at least if you accept the lower court cases as correct. The Constitution allows the police to extend the stop without suspicion for eight minutes, but not a minute longer.