When I see a police dog inside a train station or at a public gathering, I feel safer. I figure it is there to protect us from explosives, and if it sniffs out drugs along the way, well, that’s against the law, too.

But what if it turns out that the dogs aren’t all that good at the job the police are giving them? If that’s the case, should we think differently about when the police should use dogs to sniff us and our belongings, especially in the privacy of the home?

That’s the question in two cases being argued before the Supreme Court this week. In the first case, Florida vs. Jardines, the Miami police used a trained detection dog named Franky to check for drugs at the home of Joelis Jardines after getting a Crime Stopper tip. Led onto the porch, Franky sat down by the front door, his sign for alerting his handler that something smelled funny. The police got a search warrant and found a pot-growing business inside the house.

In the second case, Florida vs. Harris, a sheriff’s deputy pulled over Clayton Harris because the truck he was driving had an expired license plate. Harris was breathing fast, so the deputy asked for permission to search his truck. When Harris said no, the deputy brought his trained dog, Aldo, over to the truck, and Aldo alerted him to a smell on one of the door handles. With that as his basis for a search, the deputy looked inside the truck and found ingredients for making methamphetamine.

Both Jardines and Harris challenged the searches as violations of their Fourth Amendment rights. They argue that the police should have gotten a warrant before they deployed Franky and Aldo.

Back in 1983, however, the Supreme Court said that a dog sniff isn’t a search under the Fourth Amendment, which means the police don’t need a warrant. The idea was that dogs are sui generis as a detection method because the only information they can provide is the presence or absence of drugs. Since nothing else is revealed, there’s no privacy at stake. Key to the court’s reasoning was “the assumption that sniffing dogs do not err.”

That’s how Justice David Souter put it in 2005, in dissenting from another pro-dog ruling. Souter said, in response to the argument that dogs can only detect the presence or absence of drugs, that “the infallible dog, however, is a creature of legal fiction.” Souter’s best evidence was an Illinois study showing that trained dogs tasked with sniffing for drugs came up with false positives between 12 and 60 percent of the time.

In fact, there’d been hints of the false positive problem earlier: In Indiana in 1979, 26 trained dogs sniffed 2,780 junior high and high school students, running their noses along the kids’ legs. They identified 50 students as drug carriers. The kids were strip-searched or told to empty their pockets. Thirty-five of the 50 students were clean.

What about all the trusty hounds who go baying after their prey in detective stories? It turns out that while dogs have been used to track fugitives for centuries, they’ve only been used to sniff out drugs since about 1970, according the criminal defense bar. And according to a 2005 Queens University study, dogs may be much better at following a trail of scent over a series of footsteps than at identifying intermittent plumes of odor, which is what they are trying to detect inside a truck or behind a front door.