Bradford began to throw sidearm in high school, then dropped his arm angle even lower and became a submariner in the minors. The change was so successful that his 18 saves were second in the Chicago White Sox organization in his first year of pro ball in 1996. The strange delivery masked his mid-80s velocity, while excellent control helped him ring up both lefties and righties.
After only three years in the minors, he pitched in 29 games for the Chisox with a respectable 3.21 ERA in 1998, but still found himself back in the minors the following season. After two more extremely brief windows of opportunity (12 games in 1999 and only three in 2000) Bradford left Chicago as a free agent and signed with the Oakland Athletics, with whom he had a strong season, posting a 2.70 ERA in 66 innings of work.