In 1961, he reported to camp out-of-shape and held out before the season. The Braves placed Covington on waivers after appearing in 9 games. By this time, he had developed bad knees which would hamper his playing time for the remainder of his career. The Chicago White Sox signed him on May 10. He played 22 games for them, driving in 15 runs, with 4 home runs, and a .288 batting average. On June 10, he was traded along with Stan Johnson, Bob Shaw and Gerry Staley to the Kansas City Athletics for Andy Carey, Ray Herbert, Don Larsen and Al Pilarcik on June 10.