Stevens became a professional snooker player in 1994; in his second season, he won the Benson &amp; Hedges Championship to qualify for the Masters, where he beat Terry Griffiths 5–3 but lost 5–6 to Alan McManus. He also showed potential the following season by beating Stephen Hendry 5–1 in the Grand Prix. In the 1997–98 season, he reached the semi-finals of both the Grand Prix and the UK Championship, achieving the highest break of the tournament at the latter. He also reached the quarter-finals on his debut at the Crucible in the World Championship, beating Alain Robidoux and Mark King before losing to Ken Doherty. In 1998, he reached his first ranking final at the UK Championship, losing 6–10 to John Higgins.