Their cats feel the same way.

So some cat owners who would never dream of letting their pets roam free outside have come up with a creative compromise: an enclosed space — usually in the form of a screened-in porch or deck — that allows them to share the great outdoors.

Please don’t call it a cage. They prefer the term “catio.”

“The cats, they like to sit out there,” said Stefanie L. Russell, 44, referring to the balcony of her 12th-floor Greenwich Village apartment, where a homemade enclosure keeps her three Burmese cats safe. “Before, we basically didn’t use the balcony at all, because we were afraid that the cats would fall or jump.”

Two years ago, she and her husband, Robert Davidson, who are on the faculty of the N.Y.U. College of Dentistry, fenced off half the balcony, which runs the length of the apartment. They used industrial-grade PVC pipe and heavy black netting, creating a fully enclosed space that they decorated with furniture, plants and carpeting. Now the couple and their 9-year-old daughter, Sophie, leave the terrace door open for Oliver, Lily and Jackson, who are, as Ms. Russell put it, “the type of cats that love to run out in the hallway.” The cats seem happier, she said, and there has been an unexpected bonus: “Before, we used to have pigeons nesting on the balcony, and it was just a mess.” These days, the birds keep their distance.

Catios have made inroads in the suburbs, where they range from small, practical structures — like a box made of wood and chicken wire — to all-out fantasy cat playgrounds, replete with tunnels and scratching posts. But such enclosures remain a rarity in the city, where giving up even a square foot of real estate to a litter box can seem like a sacrifice.

Still, the forfeit felt worthwhile to Mary Sillman and Martin Stein, who set aside half their small deck in Park Slope for Buster, a 9-year-old gray cat adopted from a shelter who had been using the deck off their one-bedroom apartment as an escape hatch. “I did go and find him, but I had to climb over backyard fences and bother neighbors,” said Ms. Sillman, 55, a graphic artist. Two years ago, Mr. Stein, who is an architect, built a catio the size of two phone booths that Buster can get to through a window. “It’s just been the greatest thing for him,” Ms. Sillman said. “He just loves looking into the gardens below and people’s backyards.” Although the couple have less outdoor space for themselves, they do not mind, Ms. Sillman said. “It’s kind of like we’re sharing the deck.”

Another Park Slope resident, Rose-Marie Whitelaw, turned her entire 10-by-20-foot deck into a haven for her seven cats. Using pipes, chicken wire and deer fencing, she erected a seven-foot railing that the cats cannot climb, then spray-painted it black so it would be less obtrusive. “I’m kind of handy with copper piping and a blowtorch,” said Ms. Whitelaw, 50. She and her husband, Russell Piekarski, have an outdoor picnic table where they eat meals among the cats in nice weather. Sliding glass doors lead to a kitchen and home office, and the cats can usually go in and out all year round. “When the snow is piled to here, Julius makes tunnels,” said Ms. Whitelaw, referring to her large orange tomcat.