And if the license lottery fails them, they can always try pestering the mayor, who can issue licenses for good cause or compassion.

''It's the worst issue I deal with,'' said Mayor Tom Pollard, manager of Rustler Lodge. ''The day after I was elected I got my first call - I hadn't even gotten to the job. They disguised it as a question about garbage service, then finished with, 'Can I have a dog?' ''

To protect the alpine watershed, an ordinance in this former silver town limits dogs to 12 percent of the human population, with few exceptions. No four-legged visitors are allowed, even inside cars, and violators can go to jail.

For now, the town council keeps the lid at 42 licenses, even though it could add two more dogs under the formula tied to Alta's population of 370 old-timers, ski bums, business owners and resort employees.

''I never heard of a place limiting dog licenses,'' said Stephan Otto, a lawyer and legislative director for the Animal Legal Defense Fund, which tracks dog ordinances. ''It sounds a little European.''

And ''it's almost impossible to get one. It took me 11 years of trying,'' said Mark Hoffman, a 56-year-old lawyer and avowed ski bum. ''They'll have 17 people wanting a dog for only two or three licenses.''

Alta occupies 4 square miles inside a national forest where a special act of Congress left Salt Lake City in charge of the water supply. The city and county police the canyons, keeping out nonresident or unlicensed dogs to curb bacterial contamination of streams and protect Salt Lake's drinking water.

The scramble for dog licenses in Alta has people chatting about dearly departed Kali, who belonged to Alta's former mayor, Bill Levitt, and his wife, Mimi.

But the Levitts say they are not giving up the license. Under the ordinance, they have six months to find a new Fido to romp with kids at their Alta Lodge.

Property owners who live in Alta for at least six months of the year get first dibs on the dog licenses. Leftovers are distributed at drawings held at high noon by a town marshal, and they go next to part-time business or property owners, then lastly to seasonal employees.

It's too early to tell if any of the 42 licenses will become available in 2007, but that's why the mayor has the power of dog pardon. He can throw dog lovers a bone, granting ''compassion'' licenses temporarily and signing off on things like dogs at weddings.

''It's one of the most critical issues I ever had to face,'' Levitt, who was mayor for 34 years until last January, said of the whole dog equation. ''It is not a fun thing. I asked the new mayor, 'Do you hate dogs?' He said, 'No, I just hate the procedure.' ''

The area's handful of avalanche rescue dogs don't count against the licensed dog limit - ''as long as they have their little jackets on,'' Town Clerk Kate Black said. The same goes for service dogs for the disabled.

Maureen Hill-Hauck, executive director of the American Dog Owners Association, called Alta's ordinance ''totally ridiculous.''

''No other town limits dogs. How can people live without dogs?'' she said. ''It sounds like a total and complete violation of a person's civil rights. How dare they?''

Sometimes, despite the ordinance, a mayor just can't say no.

Sean Walton, manager of Alf's Restaurant on the slopes, shares a tiny apartment with his fiancée and her invalid German shepherd atop a lift ticket office at Alta. Their temporary dog license - their second - was good only through the end of the year. Walton and his fiance, a nurse, asked the mayor for another extension, long enough to get them to the next town drawing May 1, if anything's available.

The alternative, they said, was sending the dog back to the woman's ex-husband, a Colorado doctor who travels overseas doing surgery for Operation Smile. That would mean a future of dog kennels for 14-year-old Marta, who ''gets real lonely,'' Walton said.

Then came good fortune via the mayor.

''We're both really happy about it,'' Walton said. ''The mayor was as nice as you could expect.''

Pollard said he was giving Walton a compassion license for the remainder of Marta's life.