Jamey Wright‘s deceptively steady career will continue in the Tampa Bay Rays organization. The free agent right-hander signed a minor-league contract Tuesday with an invitation to spring training, the Rays announced.

The Dodgers let Wright become a free agent after he went 5-3 with a 3.72 earned-run average in 66 games out of the bullpen last season. The 38-year-old was second on the team in appearances (to Ronald Belisario) and games finished (to Kenley Jansen) after being slotted as a middle reliever to start the season.

Actually, Wright didn’t have a slot to start 2012. This is the eighth straight year he’ll enter camp as a non-roster invitee hoping for a major-league job. He beat out John Grabow for the final bullpen spot last year, but had even less of a chance in 2013 with right-handers Belisario, Jansen, Brandon League, Matt Guerrier, and Javy Guerra already on the 40-man roster. The Dodgers also poached free agent left-hander J.P. Howell from Tampa Bay and Wright’s historical success against lefties — no home runs in 139 plate appearances with a .252 batting average in 2012 — might mean he inherits Howell’s role out of the Rays’ bullpen.

A bigger incentive for Wright: He gets a shot with a perennial contender. In a 17-year career playing for nine teams, Wright has never pitched in a postseason game.