We’ve all seen it happen: Someone wheeling a little mesh pet carrier into a restaurant that has never allowed “doggie dining.” Or swanning through a grocery store with a dog yapping its head off in their cart or squatting in Aisle 3 to do the unthinkable. Even — for heaven’s sake — in a movie theater, with an obviously untrained, misbehaving animal running around begging for snacks.

Many businesses feel helpless against these canine invasions. The law on service animals is very clear and easy to use, but provides almost no defense to determined pet owners who are willing to lie, and even spend money on fake “service animal” harnesses. They know business owners can only ask two questions: Whether the dog is a service animal required because of a disability, and what work or task the dog has been trained to perform. And they are blithely unbothered by the legitimate health and public safety problems they spawn.

And if you think about the mindset of someone who is willing to exploit federal disability law to tote their pets into spaces where they are not just unwelcome, but specifically banned by federal and state law, it’s not hard to understand why many business owners are hesitant to crack down.

The question is: How do we fix this, without discriminating against people who have a legitimate need for service animals?

Publix has it figured out. If more businesses followed the iconic, Florida-based grocery store chain’s lead, this problem might dwindle, dramatically.

In past weeks, coverage has focused on new signs that lead off with the words, in light Publix green, “No pets allowed.” Underneath, it states “This includes emotional support animals. Only service animals are permitted.” The sign provides a concise rundown of state and federal laws, including a reminder — as tart as key lime pie — that misrepresenting a dog as a service animal is illegal in Florida and other states. Its reference to emotional support animals reminds people that dogs and other animals who fulfill mental-health needs but aren’t trained to perform specific tasks are only protected by laws referring to public transit and residential accommodations.

Setting things up this way, and making it clear to employees that they won’t be disciplined for confronting pet owners who don’t follow the rules, could do a lot to ease the problem. It’s not a perfect solution, because it opens the door to harassment against people with legitimate but invisible disabilities like post-traumatic stress disorder. But it provides a solid defense against the worst abuses: Non-disabled people who want to bring poorly controlled, untrained animals into businesses or restaurants and ignore rules about placing them in shopping carts or allow them to run free.

Publix’s policy, and its willingness to enforce the rules, is nothing new. But it’s also unfortunately all too rare.

We don’t dispute that disability rights activists have legitimate concerns about stricter rule enforcement. Aside from harassment problems, they argue that properly, officially trained service dogs are expensive, and waiting lists can be long. This is a separate challenge, and one that deserves attention. But carrying untrained animals into areas where they are prohibited by law doesn’t solve it.

We need more businesses to follow Publix’s lead. Make it clear that pets are banned. Spell out the law that requires them to be under control and trained to perform specific tasks. Empower employees to talk to customers who clearly aren’t following state and federal restrictions, and don’t be afraid to eject customers who don’t comply.

If enforcement becomes more consistent, it might not block the most brazen offenders. But it will give pause to those who encounter poorly behaved, illegal animals everywhere they go, and start to wonder why they can’t tote around their own pampered pooches.