Mondesí was originally signed by the Los Angeles Dodgers as an amateur free agent in 1988 out of the Dominican Republic. With the Great Falls Dodgers in 1990, he hit .303 with 30 stolen bases and was selected to the Pioneer League All-Star team. In 1991, he played in 21 games with the Bakersfield Dodgers, 53 games with the San Antonio Missions, and 2 with the Albuquerque Dukes hitting .277 with 8 home runs and 18 stolen bases. In 1992, he played 18 games with San Antonio and 35 with Albuquerque, hitting .296. He spent all of 1993 with the Dukes, hitting .280 with 12 homers and 13 steals.