2003. The winning bid was placed by the New York Yankees, who signed him on March 5, 2003, and assigned him to their minor league system. New York Yankees Ramírez began his minor league career in 2003 with the Tampa Yankees of the single-A advanced Florida State League. After he had a 2–8 record, a 5.21 earned run average (ERA), 21 strikeouts, and innings pitched in 14 starts, he was promoted to the Trenton Thunder of the Double-A Eastern League. With the Thunder, he had a 1–1 record, a 1.69 ERA, 21 strikeouts, and innings pitched in four games (three starts), and this earned him a promotion to the Columbus Clippers of the triple-A International League. In two games (one start) with Columbus, he had an 0–1 record, a 4.50 ERA, five strikeouts, and six innings pitched. He finished his first minor league season with a 3–10 record, a 4.43 ERA, 96 strikeouts, and innings pitched in 20 games (18 starts). In 2004, Ramírez began the year with Columbus. After he had an 0–3 record, an 8.50 ERA, 17 strikeouts, and 18 innings pitched in four starts, he was demoted to Trenton on May 1. On August 17, he allowed just two hits in a 4–1 complete game victory over the Norwich Navigators while setting a team record by retiring the last 24 hitters he faced. With Trenton, Ramírez had a 4–6 record, a 4.62 ERA, two complete games, 128 strikeouts, and 115 innings pitched in 18 starts. His combined minor league totals were a 4–9 record, a 5.14 ERA, two complete games, 145 strikeouts, and 133 innings pitched in 22 starts. Ramírez began the 2005 season with Columbus again. After he had a 1–3 record, a 5.33 ERA, 23 strikeouts, and innings pitched in six starts for the Clippers, he was demoted to Trenton for the second year in a row. At Trenton, he had a 6–5 record, a 3.84 ERA, 82 strikeouts, and 89 innings pitched in 15 starts. On July 28, the Yankees traded Ramírez and Eduardo Sierra to the Colorado Rockies for Shawn Chacón. Colorado Rockies After being acquired by the Rockies, Ramírez was assigned to the Tulsa Drillers of the double-A Texas League. He made three starts with the Drillers before getting moved to the bullpen. In 9 games (3 starts) with Tulsa, Ramírez had a 2–1 record, a 5.33 ERA, 23 strikeouts, and innings