What Dogs Don't Shed Their Fur. Dogs that dont shed bedlington terrier. Shih tzu dogs are both loyal and friendly, and they happen to be one of the small dog breeds that don't shed. Not everyone enjoys cleaning up copious amounts of dog hair. And despite its flowing locks, it sheds only minimally. Shih tzu dogs are both loyal and friendly, and they happen to be one of the small dog breeds that don't shed. If you are looking for a small dog with equally small amounts of shedding hair, .
Smart, active, and remarkably obedient, poodles are a hypoallergenic dog breed and they rarely shed.
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