HAVANA — “Is travel to Cuba for tourist activities permitted? No.” That’s what the U.S. Treasury Department website says. And yet Havana is loaded with Americans, from the Floridita bar, where they pose for photos with a bust of Ernest Hemingway, to the Rum Museum, where they swig rum samples after trudging through dim displays of old casks.

Sure, some Americans follow the rules on sanctioned travel – bringing supplies to Cuban churches or synagogues, for example, on a religious activities license. Others come on approved group tours known as “people-to-people” trips with themed itineraries like the arts.

But the 36 percent increase in American visitors here since U.S. President Barack Obama and Cuban President Raul Castro announced a thaw in relations includes many travelers who sidestep the rules. Some travel via third countries by flying to Cuba from Mexico or the Bahamas. Others fly on their own from the U.S., casually filling out paperwork for one of 12 categories of travel authorized by the U.S., without much worry that anyone will check on its accuracy.

The fact is, “there’s been almost no active enforcement” of the tourism ban under the Obama administration, according to attorney Robert Muse, an expert on the legal aspects of Cuba travel.

New Yorker Zach Chaltiel, 28, traveled to Havana from the U.S. with some buddies after graduating from law school. He researched the trip online, booked a villa through Airbnb, hired a driver, and filled out a form saying the purpose of his trip was “support for the Cuban people,” one of the 12 authorized travel categories.

“It’s so easy,” said Chaltiel as he shared drinks with friends at the Hotel Nacional, overlooking the sea as a peacock strutted by. “I just wanted to go before it becomes all Americanized.”

Two Americans peered inside Hemingway’s house, Finca Vigia, marveling at the animal trophies, bookshelves and open liquor bottles that made it seem as if the writer was still there. Nearby, Cuban students lined up for a peek and tourists from around the world took photos.

But the Americans didn’t want to reveal too much about themselves other than first names, Sabine and Anna. They’d come via the Bahamas because getting permission to travel from the U.S. seemed complicated, given their varied interests and lack of official itinerary. Mostly, said Sabine, “we’re interested in coming to a country that has been so isolated.”