Burke, who combined a mid-90s fastball with a good curve and change-up, was primarily a starter in the minor leagues, where he had two really notable seasons. In 1993, with A-Advanced Central Valley, Burke went 7–8 with a 3.20 ERA and 114 strikeouts in 119 innings. In 1995 with AAA Colorado Springs, he went 7–1 with a 4.55 ERA. During 1995, Pacific Coast League managers voted Burke as the league's best pitching prospect and the pitcher with the best breaking pitch.