Cordero began the 1998 season with the Lakeland Tigers of the Florida State League, appearing in just one game, allowing a hit to the only batter he faced before moving up to the Jacksonville Suns of the Southern League. In Jacksonville, Cordero appeared in 17 games, going 1–1 with a 4.86 ERA while earning eight saves. He returned to Jacksonville for the 1999 season, as Cordero appeared in 47 games, going 4–1 with a 1.38 ERA while earning 27 saves with the Suns before earning a call-up to the Detroit Tigers.