In 2003, Valdés defected from Cuba, where he was a member of the Cuban National team. He signed with the Chicago Cubs as a non-drafted free agent in 2004, and was assigned to the Cubs farm team of the Dominican Summer League. He posted a 7–2 record with a 0.51 earned run average in 16 games for the Dominican Cubs, holding the opponents to a .127 batting average. He also saw action as an outfielder, batting .241 with 12 doubles and 26 runs batted in in 50 games, and was selected for the DSL Post-Season All-Star.\n', '

Valdés opened 2005 with Double-A West Tenn, but was promoted rapidly to Triple-A Iowa on May 9. He went 2–0 in five starts, struck out 18 batters and issued just three walks over 23 innings of work for West Tenn. While in Iowa, he was 6–7 with a save in 25 appearances (17 starts), working six or more innings in six of his starts, ending 5–0 with a 2.15 ERA in those outings.\n', '

In 2006, Valdés dropped to 1–3 with a 7.59 ERA in 32 innings for Iowa before being released.\n', '

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