In the 1999–00 season Stevens got to all three finals of the Triple Crown events. In the final of the 1999 UK Championship he lost to Mark Williams 8-10. He won the 2000 Masters title, with a 10–8 win over Ken Doherty in the final. At the 2000 World Championship, he reached the first of his two world championship finals to date. After victories over Tony Drago, Alan McManus, Jimmy White, and Joe Swail, he faced Mark Williams in the final, losing 16–18, after having led 10–6, 13–7, and then 14–10, with the final session to play. Stevens became only the second player in the history of the world championship to lose in the final from holding a four frame overnight lead. He has also been beaten in a world championship semi-final on four occasions: in 2001, 2002, 2004, and 2012. In 2002, he looked certain to have won a place in the final, leading Peter Ebdon 16–14 in their semi-final tie, and just needing a relatively simple red in the 31st frame to leave his opponent requiring snookers. When Stevens missed the pot, Ebdon made an impressive clearance to win the frame and went on to take the next two frames to win the match 17–16.