Sometimes individual officers offered rewards for apprehension of deserters.
Example from the Huntsville Confederate, Mar. 26, 1863 --

I will give Thirty Dollars reward for the arrest and delivery to me or lodgment in jail with due notice to me, so that I can secure them, each of the following deserters from Company C, 27th Alabama Regiment, C.S.A., now at Port Hudson, Louisiana, viz:

[List of names and physical descriptions of nine soldiers.]

All of the above men enlisted at Florence, Ala., on the 24th of December, 1861.

Address

Capt. E. B. THOMPSON,
Company C, 27th Ala. Regiment, Port Hudson, Louisiana.