The title "Confederate" used by several military commands has been frequently misunderstood to mean "regular army". That's a mistake. The Confederacy didn't really raise a regular military establishment of this kind.

Organizations designated as "Confederate" always included companies from two or more states. For instance, the 1st Confederate Battalion organized for the war with five companies about March 17, 1862, at Fort Pillow, Tenn. Most officers and men had reenlisted after a twelve-month term in units leaving the service. One company had been recruited from the 36th Georgia Regiment, the rest from the 2nd Alabama Regiment.

Shortly afterwards, five more companies joined, and the battalion organized as the 1st Confederate Regiment on July 15, 1862, at Camp Vernon, Abbeville, Miss. Four new companies came from Mississippi and one more from Tennessee. The Tennessee company was a consolidation of four incomplete companies raised by Colonel B. Desha Harman at Memphis, Tenn., during March 1862. However, the Mississippi companies were soon ordered elsewhere, and this command remained in service as the 1st Confederate Battalion throughout the rest of its career.

Organized Dec. 27, 1861, at Fort Pillow, Tenn., the 4th Confederate Regiment was called Baker’s 1st Alabama-Tennessee-Mississippi Regiment. Initially the War Department recognized this command as the 39th Tennessee Regiment, probably because the regiment organized in that state. Members surrendered at Tiptonville, Tenn., Apr. 8, 1862, being released on exchange at Vicksburg, Miss., Sept. 20, 1862. Orders from the War Department dated Sept. 29, 1862, dissolved this command. Four companies were reassigned to the 42nd Tennessee Regiment, while the remaining six formed part of the 54th Alabama Regiment.

Here's the National Archives microfilm catalogue of "Confederate" military commands. Some are properly included, such as Wood's Confederate Cavalry, also known as Wirt Adams' Mississippi Cavalry, and Dent's Confederate Battery, which many people mistakenly believe to be an artillery company from Florida. Others are left off, such as Armistead's 16th Confederate Cavalry. It's listed in the Mississippi microfilm as the 12th Mississippi Cavalry.
http://www.accessgenealogy.com/military/civil/archives.htm

Since they don't really fit any one state, histories of these units can be difficult if not impossible to locate. The Alabama State Archives has an 1872 history of nearly all military units (including Confederate) recruited in this state --
http://www.archives.alabama.gov/referenc/alamilor/mil_org.html