STANDARD

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There are jus two varieties of Chihuahua - Long and Smooth Coated. They are identical bar coat, with the Long variety possessing fringing/furnishings. 
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The breed standard asks for a dainty specimen with an apple domed head, balanced and compact body, level topline, completed with a sickle tail.
 
Please see links to the breed standard below :
 
KC Standard - https://www.thekennelclub.org.uk/breed-standards/toy/chihuahua-long-coat/ 
https://www.thekennelclub.org.uk/search/breeds-a-to-z/breeds/toy/chihuahua-smooth-coat/
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FCI Standard - https://www.fci.be/Nomenclature/Standards/218g09-en.pdf
 
AKC Standard - https://images.akc.org/pdf/breeds/standards/Chihuahua.pdf
 
UKC Standard - https://www.ukcdogs.com/chihuahua
 
CKC Standard - https://www.ckc.ca/CanadianKennelClub/media/Breed-Standards/Group%205/Chihuahua-Long-Short-Coat.pdf
 
ANKC Standard - https://dogsaustralia.org.au/members/breeds/breed-standards/Chihuahua-(Smooth-Coat)
 
DogsNZ Standard - https://www.dogsnz.org.nz/breeds/info/chihuahua-smooth-coat/116#:~:text=Preferred%20furry%2C%20flattish%20in%20appearance,2%20%2D%204%20lbs)%20preferable.
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Disclaimer - ‘Deer Head’ is simply a term used by disreputable breeders to market their poorly bred stock. A responsible breeder will never use the term ‘Apple Head’ for their stock either, as this too originates in fad terminology. A Chihuahua is a Chihuahua, long or smooth, or it is not.