Cordero spent part of the 2002 season with Oklahoma, playing in 11 games, going 0–2 with a 5.84 ERA, while earning two saves. In Texas, Cordero earned his first career MLB save on June 19, 2002, striking out all three batters he faced in the tenth inning in a 7–4 win over the Chicago Cubs at Wrigley Field. He had a solid season with the Rangers, going 2–0 with a 1.79 ERA, while earning 10 saves. Cordero began the 2003 season as the set-up man for closer Ugueth Urbina, however, the Rangers traded Urbina to the Florida Marlins in July, and Cordero became the Rangers' closer. Cordero earned 12 saves during the last two months of the season. Overall, Cordero was 5–8 with a 2.94 ERA and 15 saves in 73 games pitched.