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The White Sox signed Alexander to a one-year, $760,000 contract Sunday.

Alexander was DFA'd by Milwaukee last Sunday and elected free agency after clearing waivers. He struggled during his tenure with the Brewers, posting a 6.19 ERA, 1.49 WHIP and 30:12 K:BB over 36.1 innings while picking up a hold, a save and a 3-5 record. Alexander can serve in a swingman role, as he made four starts earlier this season, including a start against Cincinnati on April 4 during which he tossed 5.2 hitless innings. In corresponding roster moves Sunday, Jared Shuster landed on the 15-day IL due to a blister, and Fraser Ellard was transferred to the 60-day injured list.

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