(CBS) -- 4-year-old Oscar is one of more than 30 French bulldogs abandoned this year at Battersea Dog's Home in London.
He's up for adoption, and next in line for surgery because he can hardly breathe with his scrunched up nostrils.
"There's this fashion for...it's almost like a Disney drawing of a dog with this sort of squashed face, these sort of protruding eyes, little skin folds," say Battersea Dog's Home head vet, Shaun Opperman.
Opperman says a celebrity craze for the flat-faced Frenchies has fueled a dangerous spike in demand that's led to overbreeding. Most of the Frenchies dropped at this charity shelter come from owners who can't afford the medical bills.
This surgery to widen Oscar's nostrils and open his airways would normally cost more than $2,000.
"A lot of them can't play with other dogs or exercise properly because they do too much, they're at risk of death really," says vet Ella Kelsey-Foreman.
7-year-old Texas is next in the operating room. He's also struggling to breathe.
"Studies show that 60% of owners aren't aware that their dogs have these breathing issues. They think this snoring spluttery breathing is normal," says Opperman.
The health issues linked to Frenchies have some vets in the UK calling for a ban on the breed, saying owning one is animal cruelty.
But Steven Hunter-Mahan says he got his Frenchie 'Teddy' from a quality breeder and that's the key.
"The best thing to do is to meet mum and dad, so you can see what their homes are like, see how they interact with the puppies," he says.
Vets hope over time French bulldogs will stop being bred for their cute features, and eventually become healthy again.