In 1962, Wilhelm had his fourth All-Star season, finishing with a 7–10 record, a 1.94 ERA and 15 saves. On January 14, 1963, Wilhelm was traded by the Orioles with Ron Hansen, Dave Nicholson and Pete Ward to the Chicago White Sox for Luis Aparicio and Al Smith. Early in that season, White Sox manager Al López said that Wilhelm had improved his pitching staff by 40 percent. He said that Wilhelm was "worth more than a 20-game winner, and he works with so little effort that he probably can last as long as Satchel Paige." He registered 21 saves and a 2.64 ERA.