For would-be patricians of the old school, only a pedigreed, purebred dog would do. Think of The Thin Man’s Asta,

For would-be patricians of the old school, only a pedigreed, purebred dog would do. Think of The Thin Man’s Asta, the wirehaired fox terrier; Jacqueline Susann’s poodle, the inspiration for her first book, Every Night, Josephine!; Lady, the cocker spaniel; 101 Dalmations. Silent-movie stars in breakfast coats swishing jauntily down Park Avenue or Sunset Boulevard, led by imperious longhaired Afghan hounds.

But now, in this era when everything from shirts to lattes to perfume must be “customizable”—why not one’s pet as well? Toodle-oo, Lhasa apsos! New York and Hollywood have gone wild for designer cross breeds. Mischa Barton, late of The O.C., has a shi-poo, a Shih Tzu crossed with a miniature poodle, while pop star and gay divorcée Jessica Simpson favors the half-Maltese malte-poo. Actors Uma Thurman, Julianne Moore, James Gandolfini, Jake Gyllenhaal and Sylvester Stallone all own “puggles”—a cross between a pug and a beagle. Restaurant entrepreneur Danny Meyer loves his labradoodle, Louie. And cuddly WNYC host Leonard Lopate and his wife Emily Hoffman, a freelance news anchor, proudly parade the streets of Park Slope with their three-year-old apricot-colored, 40-pound golden-doodle, Buddy, who resembles an overstuffed teddy bear. They got him from a breeder in Maryland. “I never say he’s a mutt,” Ms. Hoffman said.

“For a long time, these labradoodles or puggles, etc., etc., they were all thought of as outcasts, mongrels,” said Leslie Padgett, editor of New York Dog Magazine. “But now it’s cool to have a dog that not everyone else has.”

Certainly it’s hard to think of a pet that can cost up to four figures as a “mutt” or a “mongrel”—even if that, technically, is what it is. At Puppy Paradise on Flatbush Avenue, the store that sold Messrs. Gandolfini and Gyllenhaal their puggles, breed specialist Dave Barber estimates that one-quarter of revenue comes from these haute hybrids, which retail for $600 to $1,000 apiece and purportedly have more docile temperaments than their yippy purebred predecessors. “They’re small, fluffy and come in a variety of colors,” Mr. Barber said, easing any fears that a new pooch might clash with a Pucci. “A lot of customers rent a small apartment in Manhattan or Brooklyn, and they need something small. The market turns them toward small breeds.

“A lot of New Yorkers don’t have the time to walk their dogs,” he added.

Mustapha Khan, a film director, is one of the many New York dog lovers for whom fantasy ran up against reality—which is to say, realty. He always wanted a golden retriever. “If only they didn’t shed and were smaller!” said Mr. Khan, who lives in somewhat cramped Cobble Hill quarters with his wife, a jewelry designer. When he met a fellow New Yorker with a golden-doodle at the Union Square dog walk, “I thought, ‘This is perfect,’” Mr. Khan said. But then he thought, “Hey, why not one even smaller?” After a furious Internet search, the filmmaker found something called the “mini-backcross golden-doodle”—half golden-doodle, half-poodle—and in short order acquired two (one named Little Bootsy Collins, after the funk artist, the other simply Boyo).

Meanwhile, Sasha Durcan, a residential real-estate contractor who has a garden apartment in Carroll Gardens, is delighted with the low maintenance of her strawberry-blond malte-poo, Daisy (the same name that Ms. Simpson chose for her malte-poo). Because apparently malte-poos don’t, well, poo all that much. “I call her the Stepford pup,” said Ms. Durcan, who also has two children, ages 5 and 7. “She’s so easy to take care of. I keep thinking, ‘This can’t be real!’”

Now that the warm weather is here, Daisy’s owner has been happy to take her for strolls, but come winter, “I’ll probably throw her in the backyard,” Ms. Durcan said. “These poo mixes are almost the perfect mix of a cat and a dog,” she went on. “Like a cat, they’re self-sufficient, and you don’t have to walk them. I have friends who never take them out. Not that I think that’s good.”

Owners of the highfalutin’ fusion Fidos like to argue that they would have chosen a cur from the pound (really, truly) if it weren’t for the issue of dander; reputedly, the designer crossbreeds are less irritating to the mucus membranes than an ordinary hound. “If I didn’t have the allergy situation,” Ms. Durcan said, “I would have gone to the shelter.”

Oodles of Schnoodles

The man who coined the term “puggle” is one Wallace Havens, of Sun Prairie, Wis. Mr. Havens, who has been in the business for 39 years, is one of the premier breed inventors in the field. “When I first started, and people started asking what kind of puppies I had, I’d tell them and they’d just sort of laugh,” he said over the phone in a Midwestern twang.

Many competitors have since tried their hand at breeding puggles, causing Mr. Havens some ire. “If you breed a puggle to a puggle, you’ll get some puppies that will look like the pug, some that will look like the beagle—you’ll get a mess,” he said. “These dogs are not bred for breeding at all; they’re just bred to be pets.”

He’s decided to keep the “recipes” for his latest crossbreeds—the miniature Saint Bernard and a toy-dog smorgasbord he terms the “tiny mite”—top secret. “The mini Saint Bernard looks like the Saint Bernard, but it doesn’t shed and won’t get hair in the house,” Mr. Havens said proudly. “Some of the big Saint Bernards slobber, and the mini Saint Bernards don’t. They have what’s called ‘dry mouth.’” There’s already a 25-person waiting list for his creation.

But not everyone is wild about this Frankenstein-like quest for the ultimate convenient city pet. “Do we always have to go that extra step to have a dog more expensive, more unique?” plaintively asked Wendy Diamond, editor of Animal Fair magazine and owner of a purebred Maltese named Lucky. “It’s like you’re creating your own human! Is there that perfect man out there? That perfect dog?”

And, predictably, longtime pure-breed devotees turn up their noses at the fad.

“When someone tells me they want a schnoodle”—a schnauzer-poodle mix—“I’m like, ‘Why would you do that?’” said Edward Alava, a champion purebred schnauzer owner and the manager at Le Chien, a pet salon in Trump Plaza. “Schnauzers are the greatest breed. There’s all kinds of purebred dogs that already have the look the cross-breeders are going for.”

When a client asked Geri Kelly, another champion schnauzer breeder, to mate one of her dogs with a poodle, she sharply refused. “A schnauzer is known as the dog with the human brain,” Ms. Kelly said. “They’re smart, they’re intelligent, they have no body odor. Why would you breed one with a poodle?”

Ms. Kelly is further incensed by the lofty prices that some of the hybrids are fetching (a $3,000 puggle is not unheard of). “When you buy one of my dogs for $1,500, before it leaves my home, it has an eye certificate, a health certificate, its ears cropped by a professional, it has all its shots up-to-date, and it’s microchipped and shipped,” she said. “You’re getting a lot for $1,500. When you’re getting a schnoodle, you don’t get any of that, and if it inherits anything life-threatening, you can’t get your money back.”

More direly, some are concerned that genetic inconsistencies in a hybrid litter will lead to some dissatisfied customers and, perhaps, an influx of schnoodles and the like into already overtaxed rescue shelters. “We don’t like to see trends involving living, breathing beings,” said Daisy Okas, a spokeswoman for the American Kennel Club. “People don’t understand what they’re getting into. They think, ‘Oh, I’m going to get this hybrid at the pet store, and it’s going to be the best of both worlds and hypoallergenic.’ The claim that anything mixed with a poodle is hypoallergenic is a complete falsehood. The idea that you can mix a poodle with other dogs and get a specific coat type is laughable in the dog community.”

And the prevailing wisdom that designer crossbreeds have more peaceful temperaments might also be a myth. Mr. Meyer reports that his first year with Louie the labradoodle was far from easy. “He had his face and mouth into everything,” Mr. Meyer said. “He would chew and swallow almost anything, including underwear, hair scrunchies, chair legs and toilet paper. Early on, he gave me and my wife ‘leash elbow’ from all his pulling. We each ended up getting cortisone shots.”

After the ministrations of a dog trainer in Connecticut, Louie ceased to be a nuisance, but he’s still a far cry from the “perfect pet” that designer-crossbreed purveyors promise. Instead, his personality resembles that of a … well, mutt. Which, incidentally, is exactly how Mr. Meyer likes to think of him.

“The name is the only thing I don’t like about the breed,” he said.

He’s not the only owner embarrassed by the designer crossbreeds’ modish status. Josh Swiller, a writer in Carroll Gardens, often walks his girlfriend’s spunky black pup Amos, a Yorkie poo—but if anyone approaches him on the street inquiring the animal’s lineage, Mr. Swiller is under strict instructions to reply “mixed breed.” “She got him before we met, and she cringes every time someone says ‘Yorkie poo,’” he said. “It’s just so dorky! She didn’t fall in love with the breed; she fell in love with the dog.”

The couple also recently adopted an eight-week-old pit bull that Mr. Swiller found abandoned on the streets of Red Hook, which has presented its own issues. “You say you have a pit bull, and people think you’re aggressive and they don’t want to come near you or your dog,” he complained. “You say you have a Yorkie poo and you’re overly fancy.”

The solution?

“We just call them both mutts,” Mr. Swiller said. “Because, in the end, it doesn’t much matter what you call them or how much you paid. They’re still going to shit in the house.”