Inglett had been designated by the Rangers Monday to make room for Colby Lewis. He'd joined Texas on a December waiver claim from the Blue Jays.
Smith, 29 in April, posted a 6.8 K/9, 3.7 BB/9, and 4.11 ERA in 46 innings out of Milwaukee's pen this year. He also tossed a very strong 42.6 innings in Triple A - 1.27 ERA, 10.3 K/9, 1.3 BB/9. Smith had hooked on with the Brewers as a free agent after being outrighted by Boston in October of '08.