Meidroth went 3-for-5 with an RBI on Tuesday against the Rangers.
Antonacci went 2-for-4 with a walk, a double, a triple, an RBI and three runs scored Tuesday against the Rangers.
Peters went 3-for-3 with a home run, a double, two walks, three RBI and two runs scored in Tuesday's 11-7 win over the Rangers.
Taylor recorded his eighth save of the season Tuesday against the Rangers, retiring the only batter he faced.
Kay did not factor into the decision Tuesday against the Rangers, allowing four runs on six hits and two walks while striking out four over 4.2 innings.
Heim isn't in the lineup for Tuesday's game against the Twins.
The White Sox recalled Cannon from Triple-A Charlotte on Tuesday, LaMond Pope of the Chicago Tribune reports.
The White Sox placed Brazoban on the 15-day injured list Tuesday with a left lat strain, LaMond Pope of the Chicago Tribune reports.
The White Sox placed Benintendi on the bereavement/family medical emergency list Tuesday.
The White Sox recalled Nishida from Triple-A Charlotte on Tuesday.
