Jimmy was drafted by the Toronto Blue Jays in the 3rd round of the 1982 amateur draft. He made his Major League debut on April 6, 1984 and was utilized in relief situations through his inaugural year, notching 10 saves and a 4.65 ERA.
Jimmy moved into the starting rotation in 1985 and quickly became a cornerstone in the rotation, leading the Blue Jays to their first ever postseason appearance that year. More postseason appearances would follow, culminating in a World Series championship in 1992.
- All-star (1985, 1991, 1993, 1994)
- Finished 6th in American League MVP voting (1994)
- Finished 2nd in American League Cy Young voting (1987, 1994)
- Finished 4th in American League Cy Young voting (1993)
- Won American League ERA title (1987, 2.76 ERA)