I live near Baton Rouge, LA and try to keep up with the Miss. hunting laws. It's my understanding that the single shot has to have a patent date prior to 1900's and the minimum caliber is .38. I copied this from their web page:

PRIMITIVE WEAPONS
"Primitive firearms" for the purpose of hunting deer, are defined as single or double barreled muzzle-loading rifles of at least .38 caliber; single shot, breech loading, cartridge rifles (.38 caliber or larger) of a kind and type manufactured prior to 1900, and replicas, reproductions or reintroductions of those type rifles; and single or double-barreled muzzle-loading shotguns with single ball or slug. All muzzle-loading Primitive Firearms must use black powder or a black powder substitute with either percussion caps or #209 shotgun primers or flintlock ignition. Breech loading single shot rifles must have exposed hammers and use metallic cartridges. Cartridges may be loaded either with black powder or modern smokeless powder. Scopes of any magnification are allowed on primitive weapons. Sidearms are not allowed during primitive weapon season.

Here's the link: http://home.mdwfp.com/license.aspx