Question: dog breeds that are small and don't shed?
Answer: Bichon Frise. Bichon Frise, a name that translates to “curly lap dog” in French, is a petite, easy-to-maintain breed characterized by a hypoallergenic coat that doesn't shed and only has to be clipped every so often.
Bolognese. ... 
Brussels Griffon. ... 
Chinese Crested. ... 
Cockapoo. ... 
Havanese. ... 
Maltese Terrier. ... 
Miniature Schnauzer.