The Astros promoted Robertson in 1998 to the class-A advanced affiliate Kissimmee Cobras of the Florida State League. In 28 games with the Cobras, Robertson pitched 175 total innings. He also had a 10–10 record, a 3.71 ERA, and 131 strikeouts. He was again promoted the following year to the Jackson Generals of the Texas League. At one point during the season, he went six weeks without earning a victory. He rebounded from the drought and finished the season with a 15–7 record and a 3.06 ERA; his 15 wins led all pitchers in the league. After the season ended, the Houston Astros purchased his contract, effectively placing him on the 40-man roster.