Hybrid dogs, or "designer dogs," result from the mix of two or more pure breeds. Though the American Kennel Club (AKC) does not recognize cross breeds or allow mixed breeds to participate in competition, The American Canine Hybrid Club has been formed in support of hybrids. There are now over a one hundred recognized hybrid dogs.

The most popular breeds to mix with others are poodles and pugs, possibly because of the resulting cute-sounding names. The Shi-Poo (Shih Tzu/Poodle), Puggle (Beagle/Pug), and Pug-A-Poo (Pug/Poodle) are just a few examples. Dog lovers choose to mix breeds for health as well as aesthetic reasons. Breeds like the Bichon Frise are hypoallergenic and shed very little.

Thus, this breed is often utilized in the hopes of retaining its non-allergy causing genetics. The Bichon Shih Tzu, or Zuchon, is one example of a Bichon hybrid. It is important to note that hybrids are not pure breeds. They are a mix of one of more breeds. Mixed breeds are usually referred to as "mutts," but hybrids are different than mutts because both parents have documented ancestry.

The two pure breeds, Shih Tzu and Bichon Frise, have positive and negative traits. The Shih Tzu is a small, sturdy dog with a double coat of long silky fur. This breed is very alert and intelligent, and also very stubborn. Shih Tzu may have health problems such as frequent eye infections, inability to withstand high temperatures, and fur that is prone to matting and tangling if not either brushed daily or given a "pet clip", which is a short haircut done only if the dog is not in competition.

Bichon Frise dogs are white, fluffy "powder puffs" with cotton ball-like fur, black eyes and noses, excitable, happy temperaments. Their fur does not shed and they are hypoallergenic. Bichon have health problems such as anemia, dental problems and severe allergies though they themselves are hypoallergenic. Bichon Shi Tzu mixes are usually born with soft, curly and hypoallergenic coats, which are a mixture of both parents. Like the Bichon, they have happy temperaments, and like the Shih Tzu, they are intelligent, alert, and stubborn. They are thought to have fewer health problems then their purebred parents.

Proponents of the Bichon Shih Tzu, such as the American Canine Hybrid Club, most likely dream of the day when hybrids can be viewed as their own pure breed. Many pure breeds are the result of cross breeding.

The Bichon Frise can be traced back to 600 B.C. Descended from dogs called Barbichon in the Mediterranean. Spanish sailors took the 'Bichon' out to sea because of the breed's happy temperament. The breed made its way to Europe and the French added "Frise" to the name to reference the breed's curly fur. The Bichon was recognized by the French Kennel Club in 1934 and the American Kennel Club officially recognized the breed in 1973.

The ancestors of the Bichon Frise date back further, to 600 B.C. The Barbichon were Mediterranean dogs. Later, descendants of the breed went to sea with Spanish sailors and the name was shortened to Bichon. They migrated to Europe and the French added "Frise" to the name to reference the breed's curly fur. The Bichon Frise dog was recognized as a breed by the French Kennel Club in 1934 and the American Kennel Club followed suit in 1973.