 He made his North American professional debut with the AHL's Moncton Hawks in the 1988–89 season, and also appeared in two NHL games with the Winnipeg Jets that same season.On February 28, 1991, the Jets traded Draper to the St. Louis Blues for future considerations, which on May 24, 1991 turned out to be for Jim Vesey; Draper was ultimately traded back to the Jets.On June 22, 1991 the Buffalo Sabres acquired him from the Jets for the seventh round draft pick in the 1992 entry draft.