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Greyhound
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The greyhound is a large, athletic, powerfully-built dog that is classified as low shedding. They are noted for their speed and can run at speeds of up to 40 mph. They are gentle and intelligent dogs, renowned for being nonaggressive. Primarily bred for dog-racing, they are also good family pets due to their short-haired, low-shedding coat and gentle demeanor.
Basenji
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The basenji belong to the hound group and are smooth-coated, finely-boned dogs popular for showing in dog shows. They are unusual among dogs in that they don't bark but they do make other dog noises and can yodel. They are noted low-shedding dogs and are alert, affectionate and curious. They wash themselves like cats and are great for people with allergies.
Belgian Griffons
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There are two types of Belgian griffons -- one with a dense coat and one with a short, smooth coat. The short, smooth-coated Belgian griffon is also known as the Petit Brabancon variety. This short-coat variety is easy to groom and a low-shedding breed. The griffon is a small, sturdy toy dog often likened to the Ewok characters in the "Star Wars" movies, as it has a short pug-nosed hairy face. They are intelligent and cheerful with a terrier-like disposition and make good watchdogs.
Xoloitzcuintli
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The xoloitzcuintli, or "Mexican hairless," is known for being very low-shedding. They 'xolo' is usually a hairless dog although there are varieties of short-haired xolos. They are one of the world's oldest and rarest breeds and originated in Mexico. Mummies of xolos have been found in ancient Mayan caves and have been dated back to 3000 B.C. They are very intelligent dogs and can be trained to a high level of obedience. They are also alert, lively and affectionate.
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Short-Haired Dog Breeds That Don't Shed
All dogs shed their hair to some extent, whether they have long-haired shaggy coats or are short-haired. All dogs have hair that grows to a predetermined length and then stops growing. It is then pushed out by the new hair growing up from underneath. While there is no such thing as a non-shedding dog there are dog breeds that shed considerably less than others. These breeds can be highly sought after as high shedding can be an off-putting factor for dog owners and can also be a problem for allergy sufferers.