Núñez signed with the Los Angeles Dodgers in 2006. He pitched in the rookie-level Gulf Coast League for the GCL Dodgers, where he accrued a win-loss record of 6-0 and an ERA of 1.58 in 7 starts and 3 relief appearances; he struck out 56 batters in 57 innings. The Los Angeles organization recognized Núñez as their top minor league pitcher for the month of July. On August 31, 2006, he was acquired by the Washington Nationals for veteran utility player Marlon Anderson.\n', '

In 2007, Núñez pitched for the Hagerstown Suns of the Low-A South Atlantic League. He logged 105⅔ innings in 22 starts and one relief appearance, winning 4, losing 6, and recording a 4.05 ERA.\n', '

In 2008, Núñez pitched for the High-A Potomac Nationals and Double-A Harrisburg Senators, converting to relief. On July 31, 2008, Núñez was traded to the New York Yankees for infielder Alberto Gonzalez and joined the Yankees Double-A affiliate, the Trenton Thunder.\n', '

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