The Texas Rangers announced a one-year, minor-league contract with right-handed pitcher Jamey Wright on Saturday. Wright, who turned 40 in December, recently said he checked in with the Dodgers (apparently that’s as far as it went) and heard from about five other teams in total.

Wright went 5-4 with a 4.35 ERA for the Dodgers last season. Now, he’ll be in a familiar position: Prior to last year, he went to spring training on a minor-league contract eight straight seasons with seven different teams, including the Dodgers in 2012. Each time, he had a major-league contract by April.

Wright made 66 appearances for the Dodgers in 2012, going 5-3 with a 3.72 ERA. He elected to sign a minor-league deal with Tampa Bay in 2013 and had one of the best years of his career at age 38: A 3.09 ERA (and 3.13 FIP, both career lows) in 66 appearances, including one start.

Dodgers general manager Ned Colletti decided to give Wright a second chance as a long reliever, but he never quite filled that role. Wright excelled against left-handers (.238/.317/.303) but struggled against righties (.299/.362/.375), and became more of a situational reliever in the second half.

When the Dodgers acquired Adam Liberatore from Tampa Bay to join Paco Rodriguez for depth behind the primary southpaw reliever, J.P. Howell, it left little room for Wright to return in 2015.

The Dodgers’ bullpen ranked in the bottom half of the majors in several categories last season, like WHIP (20th), ERA (22nd), strikeout/walk ratio (25th) and strikeouts/inning (16th). Their relievers had an 18-24 won-loss record, which is remarkable considering their starters went 76-44. That’s a huge disparity in winning percentage.

Not surprisingly, the Dodgers’ bullpen will look very different in 2015.