Prior to playing professional baseball, Greene attended Coral Gables High School and then Louisiana State University. He helped lead LSU to victory in the 1991 College World Series.\n', '

Originally drafted by the New York Yankees in the 14th round of the 1989 draft, Greene chose not to sign. However, when he was chosen 16th overall in the 1992 draft by the Detroit Tigers, he did sign.\n', '

He competed in the 1992 Barcelona Olympics, so he did not play professionally that year. He began his professional career in 1993, splitting time between the Lakeland Tigers and London Tigers. In a combined 49 relief appearances, he went 4-5 with a 6.33 ERA. In 1993, he was ranked the sixth best prospect in the Tigers organization by Baseball America. In 1994, he split the season between the Lakeland Tigers and Trenton Thunder, going 1-5 with a 5.64 ERA in 39 games. That year, he started the only two games of his professional career and he was ranked the fifth best prospect in the Tigers organization by Baseball America. He also earned the first save in Trenton Thunder history that season. He showed a marked improvement in 1995 while pitching for the Jacksonville Suns. For them he went 6-2 with a 3.49 ERA in 32 appearances. He again pitched for the Suns in 1996, going 2-7 with 30 saves and a 4.98 ERA in 57 appearances and earning an All Star berth. In 1997, he played for the Toledo Mud Hens, going 6-8 with a 2.83 ERA in 57 games. On November 20, 1997, he was traded with Mike Myers and Santiago Perez to the Milwaukee Brewers for Bryce Florie and cash.\n', '

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