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Is this the face of a fraud?

You may now file hypoallergenic dogs under Things That Are Too Good to Be True. That’s the conclusion of a new study by Henry Ford Hospital researchers, which finds that homes with so-called hypoallergenic dogs don’t have lower household levels of allergens than those with other breeds.

Hypoallergenic dogs, which include purebreds like poodles and Portuguese water dogs, along with increasingly popular mixed breeds like labradoodles (the offspring of a Labrador retriever and a poodle), are thought to shed less fur and to produce less of the stuff that triggers allergies, such as dander and saliva. The price tag for these allergy-free pooches usually tops $2,000, but the new study suggests your money may be misspent if you’re buying them in hopes of avoiding allergy attacks.

“We found no scientific basis to the claim hypoallergenic dogs have less allergen,” said Christine Cole Johnson, chair of Henry Ford Hospital’s department of public health sciences and senior author of the study, in a statement.

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Although some previous research has suggested that exposure to dogs during infancy may help prevent children’s development of allergies later, “the idea that you can buy a certain breed of dog and think it will cause less allergy problems for a person already dog-allergic is not borne out by our study,” Johnson said.

For the study, researchers collected dust samples from the carpets and floors of baby’s rooms in 173 homes one month after a newborn arrived home. Each home had only one dog; 60 breeds were involved in the study, 11 of which were hypoallergenic. Johnson and her team tested for the primary dog allergen, Can f 1.

In comparing homes with dogs that were bred to be hypoallergenic to those with other mixed-breed and purebred dogs, the researchers found no significant difference in allergen levels among them. In fact, in homes where parents said the dog was not allowed in the baby’s room, allergen levels from hypoallergenic breeds were actually slightly higher than from non-hypoallergenic counterparts; perhaps parents were more apt to bend the rules if they believed their dog was hypoallergenic.

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Despite the study’s findings, labradoodle-breeder Gail Widman says she has seen many pet-allergic clients take her puppies home with good results. Recently, a family who said their 10-year-old daughter was allergic to dogs found that she had no reaction when exposed on four separate occasions to a labradoodle; they happily went home with a puppy. Widman says another client from Seattle, who had extreme dog allergies, also purchased a labradoodle puppy; he broke out in welts whenever the puppy licked him, but said the dog didn’t trigger breathing problems like other breeds did. He later reported to Widman that his allergic reactions to the dog decreased over time.

“It makes an extreme difference for people with allergies,” says Widman, founder and president of the Australian Labradoodle Club of America and owner of the Whispering Winds kennel, where she breeds the dogs. In her experience, Widman says, her breed produces less dander than other types of dogs.

The Henry Ford study’s authors acknowledge that their study had a few limitations: it did not record how long dogs spent in babies’ bedrooms, and its sample size was too small to come to firm conclusions about specific breeds.

MORE: Study: Living With Pets May Protect Infants From Allergies

But ultimately, early exposure to a pet — hypoallergenic or not — may not be a bad thing, if as some studies suggest, exposure in infancy helps safeguard some babies from future pet allergies. For adults who already have full-blown allergies, though, relying on the hypoallergenic label may be no guarantee.

Meredith Melnick is a reporter at TIME. Find her on Twitter at @MeredithCM. You can also continue the discussion on TIME’s Facebook page and on Twitter at @TIME.

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