He matured into a control pitcher, being selected to the 1980 All-Star Game. While he was pitching on September 30, 1980, he was caught using a thumbtack to illegally cut the ball. He was ejected and suspended for 10 games. Following the 1980 season, he was traded with Larry Cox, Willie Horton, Mario Mendoza and Leon Roberts to the Texas Rangers for Brian Allard, Rick Auerbach, Ken Clay, Jerry Gleaton and Richie Zisk. In 1983, Honeycutt represented the Rangers in the All-Star Game. On August 19, 1983, Honeycutt was traded from the Rangers to the Los Angeles Dodgers for Dave Stewart and Ricky Wright. Honeycutt led the American League in ERA in 1983 with 2.42, although he was traded to the Dodgers late in the season.