The act of "cropping" the ears is removing a portion of the ear flap to cosmetic purposes.
An undercover journalist was told by a breeder that it had created a striking look for the American bully breed.
This is illegal in the UK. However, breeders offer fake pet passports to suggest it was done overseas.
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One breeder suggested that he would sell an undercover journalist from BBC Wales a puppy for PS13,000 and also mentioned the possibility of cutting the ears of the dogs, which is prohibited in the UK by the Animal Welfare Act.
Paula Boyden from Dogs Trust stated that there was no reason for this practice and it could cause health and behavioral problems in the dogs.
She said, "Some animals get infections and don't like people touching them."
"We have also observed behaviour problems in dogs because they communicate with their ears. Without them, it may be difficult for them to communicate with their owners and other dogs."
Warning: Unsavorable contentBBC Wales Investigates found a number breeders posting images of cropped-eared puppies online.
Moheiz Adam, a breeder, stated that it was "a shame” cropping was illegal because it gave dogs a "striking" look.
He offered to buy a puppy from an undercover journalist for PS13,000 and stated that it would include a pet passport as well as a microchip.
"[Another person] simply takes care of it, brings it back the paperwork... If you are asked questions, you will basically [say] that you bought it from an Irishman. It came from Europe, and that's all you need to know.
He said that all of his dogs were done by him, and that it looked 10 out of 10.
During a video conference, Adam held the puppy up and said, "That will all come off."
Daniella Dos Santos (ex-president of the British Veterinary Association) commented on the evidence presented by the BBC.
"Cropping ears is illegal mutilation. It is done only for cosmetic reasons. The whole conversation has been about how the dogs look.
It's all about status. These dogs have no health benefits."
Later, Mr Adam stated that while he would like to remove dogs' ears, it was illegal and that he had never arranged for it. Joshua Harty, a Cardiff-based breeder, said to an undercover journalist that he could also arrange cropping and provide a foreign microchip and pet passport.
"To get the ears, the passport, and the chip it is usually around PS500... my vet sends them from Turkey.
"I have taken dogs to shows in Ireland and Spain and obviously I have had to cross border. I've taken these passports, and I've been through every time. He said that he has never had to deal with a problem.
Daniella Dos Santos stated that Mr Harty was suggesting "facilitating a crime."
She stated that it was all illegal to crop ears and create false passports. It is a dodgy system.
"Yet again, considering these animals as commodities and money-making machines rather than living sentient creatures."
She said that the reason this is happening was because of a loophole which allows dogs to be imported with cropped ears. This is just a smokescreen for it actually happening in the UK.
BBC Wales reached out to Mr Harty, but he didn't respond.
After their ears were trimmed, the puppies were valued at PS1,500 more.
Ms Waddon stated that she was concerned about demand being driven by social media influencers who post images of cropped-eared canines, including Marcus Rashford and Little Mix singer Leigh-Anne Pinnock, as well as Jack Fincham from Love Island.
She said that celebrities often post pictures online and people think "oh, that dog looks nice, maybe I'll buy one like that."
"While celebrities may have legally imported the dogs, there are still people who illegally grow the dogs in the UK to supply the demand."
BBC Wales reached out to representatives of Mr Rashford and Ms Pinnock, but they did not get a response. The proposed Kept Animals Bill would prohibit the importation or breeding of puppies less than six months old and dogs with cropped ears.
A spokesperson for the Welsh government stated that it has a five-year Animal Welfare Plan for Wales, which aims to combat illegal dog breeding.
Ms. Boyden stated that the law will not be enforced if border personnel do not inspect imported dogs.
She said, "A ban on importation should be welcomed. But a law can only be as good as its enforcement. At the moment there are no details on how resources will be used to check for cropped ears and if they appear underage."
Ms Waddon said, "We work with exceptional enforcement officers. They just don't possess the resources to investigate every case that has been reported to them.
"Even the best legislation can't be effective if it isn't enforced."