Cordero suffered through an injury plagued 1996 season, as he made only two starts with the Jammers, going 0–0 with a 0.82 ERA in 11 innings pitched, then with the Generals, he appeared in two games, making one start, going 0–0 with a 2.57 ERA in seven innings pitched. He played the entire 1997 season with the West Michigan Whitecaps of the Midwest League, where Cordero was converted into a closing pitcher. In 50 games, Cordero had an excellent season, going 6–1 with a 0.99 ERA in 54.1 innings pitched, earning 35 saves.