Cotts attended Illinois State University where he won first-team All-Missouri Valley Conference honors and was named to the ABCA All-Midwest Region team. He was drafted by the Oakland Athletics 69th overall in the 2nd round of the 2001 draft, becoming the second highest player drafted in the history of Illinois State. Cotts finished his collegiate career ranked fifth all-time in school history in strikeouts with 263 in just three seasons with the Redbirds.

Cotts spent the 2002 season at Single-A Modesto of the California League, winning 12 games in 28 starts. During the off-season, he was traded to the Chicago White Sox in a six-player deal involving relief pitchers Billy Koch and Keith Foulke. Cotts began the 2003 season ranked as the number three prospect in the White Sox farm system. He started his year at Double-A Birmingham, of the Southern League, going 9–6 with a 2.12 ERA and 131 strikeouts. In July 2003, he started for the United States in Major League Baseball's Futures Game.

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