Báez was signed by the Cleveland Indians in 1999. In his second season, he played for both the Indians and the Triple-A Buffalo Bisons. In his debut, he went a scoreless inning against the Tampa Bay Devil Rays. Over the rest of the year, he went 5–3 with a 2.91 ERA.\n', '

In 2002, Báez was moved into the starting rotation of the Indians. He won his first start on April 5 of that year facing the Detroit Tigers. In 26 starts, he went 9–10 with a 4.44 ERA. He was given the role of closer in August, where he finished off the season.\n', '

Báez pitched for the Indians as a reliever in 2003. He was both a setup man and a closer that season. He had 25 saves and 10 blown saves, which was tied for the most in the Major Leagues.\n', '

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