If there was a “next No. 1” need for the Detroit Tigers after they got themselves a closer, it was bolstering left field.

They may have gotten a lower-end fix to the problem than some were expecting, though, with Sportsnet.ca’s Ben Nicholson-Smith reporting Tuesday morning that the team had agreed a two-year deal with 33-year-old Rajai Davis.

Fox Sports’ Jon Morosi had reported earlier from Winter Meetings that the deal was imminent.

That’s a clear departure from where some expected them to go, not exactly chasing the big-money free agents. Compared to bidding for the top tier of free-agent outfielders — including Jacoby Ellsbury (who signed with the Yankees for seven years, $153 million) and the as-of-yet unsigned Shin-Soo Choo — a guy like Davis is shopping at a thrift store. The 33-year-old Davis made $2.5 million last season.

Tigers general manager Dave Dombrowski had indicated, however, that the Tigers’ spending spree might be over after signing closer Joe Nathan.

“I would think that we would not be involved in the big free-agent market,” Dombrowski said at the news conference to introduce Nathan.

“Again, we’re on Dec. 5, but I don’t anticipate any of the major names that our out there, that our name’s attached with, I don’t anticipate those be our signings.”

Davis would be ideal for a platoon with current left field incumbent Andy Dirks, who played all of last season with a lingering injury to his knee. Davis is a career .294 hitter against left-handed pitching (with a .779 OPS) and a .255 hitter (.650 OPS) vs. right-handers.

He does also bring some speed to the base paths, stealing more than 40 bases in five of the last six seasons.