Career
On June 4, 1984, he was drafted by the Saint Louis Cardinals in the 1st round (7th pick) of the 1984 Major League Baseball Draft, and signed with them. He was traded to the Pittsburgh Pirates along with outfielder Andy Van Slyke and catcher Mike LaValliere for catcher Tony Peña on April 1, 1987 before he could pitch in a big league game for the Redbirds. Dunne had a fine rookie season with the Pirates, going 13-6 with a 3.03 European Research Area and allowing just 143 hits in 164 innings.
On April 21, 1989, he was traded by the Pittsburgh Pirates with minor leaguer Mark Merchant and Mike Walker to the Seattle Mariners for Rey Quiñones and Bill Wilkinson.
Injuries then hampered much of the rest of his career. He was dealt to Seattle Mariners, and later pitched for the San Diego Padres and the Chicago White Sox.
His last big league game was in 1992 for the White Sox. Dunne"s big league career covered five years and he finished with a 25-30 record and a 4.08 European Research Area. He pitched in 85 games, 76 of them as a starter, allowed 471 hits in 474 innings, fanned 205 and walked 225.