[2] Stefanson was a member of the Winnipeg city council from 1982 to 1989 for the St. Charles riding, serving as Chair of the Finance Committee from 1984 to 1986 and Deputy Mayor from 1986 to 1988.
On May 9, 1995, he was relieved of the Treasury Board portfolio and given responsibility for the Manitoba Lotteries Corporation Act (remaining Minister of Finance).
[1] In a cabinet shuffle on February 5, 1999, Stefanson was appointed Minister of Health and Deputy Premier, also retaining responsibilities of the Boxing/Wrestling Commission and Fitness/Amateur Sport Acts.
On September 7, 2000, Stefanson resigned from the legislature[1] to provide a seat for the party's incoming leader, Stuart Murray.
In 1998, Stefanson was accused by some of exercising undue ministerial influence in the appointment of his brother, Tom, as CEO of Manitoba Telecom Services; no formal charges of impropriety were made, however.