20 Dogs That Don’t Shed: Hypoallergenic Dog Breeds Everybody loves a fuzzy dog whose fur feels as soft and lustrous as velvet. Like walking clouds and cotton candies, one cannot help but find these dogs irresistibly cute and huggable! However, owning a dog is not always rainbows and glitters, especially if your dog sports a thick double coat. Anyone who owns a Siberian Husky or an American Eskimo Dog knows what I am talking about: molting hair 24/7. With a smug glow of victory, many vacuum-clad owners win their daily battles against dog hair effortlessly. Unfortunately, 10% of US citizens suffer from dog allergy and have deprived themselves the loving company of a Did you know that the Bichon Frise is the ultimate lap dog? Pronounced as bee-shon free-zay, the breed’s name actually stands for “curly lapdog” Bichons sport an entirely white hypoallergenic coat of hair, not fur. Its iconic puffy look is due to its double coat This little darling sheds little to no hair. With the proper haircut, the Bichon Frise is a breeze to maintain.