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Gleaton was the Rangers' first-round draft pick in June of 1979, signed out of the University of Texas. After the 1980 season, he was included in an 11-player trade to Seattle that featured Rick Honeycutt and Richie Zisk. Gleaton was released by the White Sox before finding a home as a set-up man in the 1987 Royals bullpen.

Gleaton stayed in Kansas City for three years, the last of which (1989) was marred by two demotions to Triple-A Omaha. Dealt to Detroit the following April, Gleaton found a niche with the Tigers and set a career high with 13 saves.

Gleaton pitched well again the next season, but Detroit didn't offer him enough money to stay in 1992. Although he remained confident in his abilities -- the 34-year-old veteran told Baseball Weekly in March that he was throwing harder than he had been a decade earlier -- a brief stint with the Pirates that season proved to be his last taste of major-league action. (NLM/JGR)