Randall was a two-time All-SEC selection and an All-America honoree in doubles. He earned a top 10 ranking two years and reached the quarterfinals of the NCAA Doubles Championships in 1988. Randall and his teammate, Jamie Booras were the first tennis All-Americans at the university.
He won three SEC titles in his career at Ole Miss, including the 1988 No. 1 singles crown, and helped lead the Rebels to their first NCAA Team Championship appearance in 1989.
Randall spent nine years on the ATP Tour. He is currently the director of tennis at River Hills Tennis Club in Jackson.