Compiled Service Records. Yankees have them, too.
Just click below or in the box at the top of the page. I recall ordering one from the National Archives for my mother's ancestor when I was still in high school. War Department cards and papers made quite an impression then.
When you order remember that there are two CSRs for E. L. Richmond -- Co. "B", 17th Missisippi Regt. and Co. "E", 3rd Mississippi Cavalry.