Stevenson's best season average was 42.1 yards per punt in 1996, when Florida won the Southeastern Conference (SEC) title with an undefeated 8–0 conference season, and defeated the top-ranked Florida State Seminoles in the Sugar Bowl to win the consensus national championship. During the 1997 season, he handled both the punting and kickoff duties for the Gators. Stevenson proved to be a weapon on kickoffs, with twenty-one of seventy-one kickoffs resulting in touchbacks, and over half of his kickoffs reaching the opposing goal line or beyond.