In addition, that site shows a William Crisp and a John Crisp as members of Street's cavalry company. John Crisp is noted as killed.

This is from the following list:
"The number of men who served in Street's company is not definitely known. No muster rolls are extant, and indeed it is doubtful if any were ever made. In 1894 survivors made up from memory a roster of 69 officers and men, seven of whom were killed in action."

Also note that this is a State of Mississippi unit, formed under the authorization of the Governor. It was not transferred to Confederate Army service, until February 5, 1864, when it became a part of Stewart's 15th Tennessee Cavalry. Thus, Moses Crisp was not in the Confederate Army, but rather in the Army of the State of Mississippi, fighting for the Confederate cause.