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The White Sox selected the contract of Peralta from Triple-A Charlotte on Sunday.
Peralta was DFA'd by the White Sox on May 28 after being claimed off waivers two days earlier. After being outrighted to Triple-A on May 30, Peralta has responded with three scoreless outings, allowing no hits and one walk while striking out five over 3.2 innings in that span. He'll provide left-handed depth out of the bullpen for the White Sox with southpaw Shane Drohan (shoulder) designated for assignment and right-hander Nick Nastrini optioned to Triple-A Charlotte in corresponding moves.