In 1959, he won 20 games (losing 10) with a sparkling 2.84 earned run average for the Class B Wenatchee Chiefs.

Then, in 1960, he went 19–8 (3.57) for the Double-A San Antonio Missions and was named the Texas League's pitcher of the year.

In his rookie campaign, 1961, Curtis took a turn in the Cubs' starting rotation and won ten games, tied for second on the team.

On April 30, Curtis was traded even-up for veteran Braves' starting pitcher Bob Buhl, a former National League All-Star.

At the end of the season, he was traded again, this time to the Cleveland Indians, who had just hired manager Birdie Tebbetts away from the Braves.