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Poodle
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When most people think of a dog that doesn't shed, they think of a poodle. While it's true that poodles don't shed, it's also true that poodles come in many sizes, not all of which are considered lapdog-sized. Poodles small enough to be considered lapdogs are toy poodles, teacup poodles, French poodles, pudles, caniches, barbones, chien Cannes, and Teddy poodles. Because they don't shed, lapdog-sized poodles require grooming every six to eight weeks.
Maltese
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A Maltese is a wonderful companion dog, known for being lively, gentle and intelligent. They have long hair that does not shed, but it does require daily grooming. Pet owners who prefer not to brush their Maltese every day can choose to have the dog's hair clipped short. The dogs are protective, and will bark at just about anything. While they make great companion dogs, they're also subject to many health problems, including extreme sensitivity to hot and cold, eye problems and digestive issues.
Shih-Tzu
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Shih-Tzus are playful, spunky and affectionate, and they're one of the most popular dog breeds in the United States. Having a long-haired Shih-Tzu means daily grooming and keeping a top-knot in the dog's hair so that it doesn't cover his eyes and obstruct his vision. These dogs can be kept in a puppy cut their whole lives to make grooming easier for the owner. Shih-Tzu's are a good choice for an active dog owner, because they require daily exercise.
Chinese Crested
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One type of Chinese crested dog is hairless, and as such does not shed. The other type, the powder puff Chinese crested dog, has hair but is in the non-shedding category. The hairless dogs are prone to sunburn, and both are subject to weight problems and developing dental problems. Chinese crested dogs are known for being affectionate, charming and playful. They are a rare breed, which makes them one of the most expensive dog breeds on the market.
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Lapdogs That Don't Shed
Lapdogs are small enough to fit comfortably on a person's lap. While most lapdog owners enjoy snuggling with their dog, they don't like to be covered with dog hair afterward, so a non-shedding lapdog is ideal for them. Non-shedding does not mean that the dog is hairless, it means that for practical purposes the hair on the dog rarely falls out.