He was a part of a big trade on November 2, 1999, where the Texas Rangers traded Patterson, Juan González and Gregg Zaun to the Detroit Tigers for Justin Thompson, Francisco Cordero, Gabe Kapler, Bill Haselman, Frank Catalanotto and minor leaguer Alan Webb.
Turnbow struggled with his command through the 2006 season, however, converting only 1 of 5 save opportunities and posting a 21.32 ERA in July 2006, and causing manager Ned Yost to remove Turnbow from the closer role in favor of Francisco Cordero.
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.
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On July 26, 2006, Mench hit a 2-run double against the New York Yankees, the 50,000th hit in Rangers franchise history; two days later, he was traded to the Milwaukee Brewers along with Francisco Cordero, Laynce Nix, and Julian Cordero, for Carlos Lee and Nelson Cruz.