The Brewers, even after adding about $2.5 million in salary in the Francisco Rodriguez trade, are pursuing improvements on the left side of their infield, according to major-league sources.

No deal is close due to the limited availability of quality shortstops and third basemen, and the team will determine its remaining payroll flexibility on a case-by-case basis, sources say.

The Brewers’ search for left-side infielders is understandable – the team ranks 11^th in the National League in OPS at short with Yuniesky Betancourt, and last in the NL at third with Casey McGehee.

Both Betancourt and McGehee also are below-average defenders, advanced metrics say. Defense is a priority for the Brewers as they try to enhance their pitching, which they improved with the addition of Rodriguez.

Dodgers infielder Jamey Carroll, one possible fit, is not yet available, sources say. Orioles shortstop and former Brewer J.J. Hardy, another logical target, is expected to sign a contract extension with Baltimore rather than be traded, sources say.

Royals third baseman Wilson Betemit, a switch-hitter, also could make sense for the Brewers. Betemit, however, has struck out in 16 of his last 36 at-bats, perhaps due to the difficulty of adjusting to a reduced role following the promotion of Mike Moustakas.

A number of other infielders should become available prior to the July 31 non-waiver deadline. The Brewers want a clear upgrade, ideally a difference-maker. As they showed with K-Rod, they are willing to be aggressive.

-Ken Rosenthal