Mary -
Have fun with the grandkids, but when you get back to this project, here's what I just found:
Source: "Supplement to the Official Records" (Mississippi volume - forgot to write the precise citation). Cook's Company was formed per Special Orders No. 124, Para. 14, dated HdQrs Dept. of Alabama, Mississippi & East Louisiana, May 3, 1864. Greenville Cook was elected Captain on May 25,'64 (resigned Nov. 10,'64), and is believed to have been formed from absentees from Co. F, First Mississippi, and some recruits. Stationed at Brookhaven, Miss. on June 26,'64. That's all there was. I can't attest the truth of this, sounds a bit like post-war clerks making some deductions, but this may be 100% o.k.
John