Several screens of names will appear. About the fifth (not sure) screen, you'll note "J.K. Smith" in "Grace's Company."
If you click on "Grace's Company," you will be taken to a page that has a link for a roster of all the men (about 96) in this company.
Howell (list of MS CS soldiers) says: "4th Corporal J.K. Smith, Capt. Grace's Company, MS State Troops, Independent Cavalry."
Military History of MS says: "Unattached (Cavalry) -- Grace's Company. Captain W.G. Grace, organized September 14, 1864, discharged March 15, 1865."
However, bear in mind that there is a Capt. Grace's company of independent cavalry and a Capt. Grace's company of independent infantry, so things can get mighty confusing!
A J.K. Smith filed for a CS Pension in 1922 in Neshoba County, MS, but did not state his unit on his application.
Wish I could have helped you more! I'm afraid I've just confused things even more! -- Jim Huffman, Gainesville Vols