McDougal was optioned to Triple-A Charlotte on Saturday. The right-hander gave up a hit and a walk in 1-3 inning in the first game of Saturday's doubleheader, a 5-1 loss to Baltimore.
McDougal has a 2.08 ERA this season, with seven walks and seven strikeouts in 8 2-3 innings. He had a 6.80 ERA in 54 appearances with Chicago last season.
White Sox manager Ozzie Guillen said he wants the erratic McDougal to work on his fastball in the minors.
Wassermann hadn't allowed a run in eight appearances at Charlotte, picking up six saves and 10 strikeouts.
