The Company Muster Roll of one of my wife's ancestors (Samuel G. Dupre) indicates that he enlisted in:
Capt. W.B. Denson's Cavalry Company, Unattached Brigade.*

at the bottom of the Company Muster Roll it says:
* This company subsequently became Company A, 6th Regiment Louisiana Cavalry.
The regiment was first organized in the Trans-Mississippi Department during the winter of 1863-64, as Harrison's Battalion Louisiana Cavalry. It was increased to a regiment by the addition of unattached companies and designated the 6th Regiment Louisiana Cavalry.