Jeffcoat’s first full season was spent as a long reliever for the 1984 Indians (5-2, 2.99). A May 1985 trade sent him to San Francisco with infielder Luis Quinones for Johnnie LeMaster, but the lefty pitched sparingly for his new club and spent 1986 in Triple-A.
Released in October, Jeffcoat signed with the Rangers. He pitched mainly in the minors before earning a big-league rotation spot in 1989, but despite a solid performance (9-6, 3.58) he was back in the bullpen by the end of the following year. Jeffcoat made 70 relief appearances in 1991, his last productive season in the bigs.