The Brewers have agreed to a one-year deal with left-handed reliever Michael Gonzalez, according to a Friday FOX Sports report. Gonzalez, 34, flourished last season with the Nationals as a mid-season addition on a one-year minor league deal and pitched in key situations against left-handed batters down the stretch. According to a CBS Sports report, his deal with the Brewers is worth $2.25 million with incentives, marking the second Nationals left-handed reliever to head to Milwaukee  a team starved for them.

Again, the Nationals lost out on bringing back one of their own relievers, choosing not to pay in a market where left-handed relievers are at a premium. Instead, they are left with only one left-handed reliever on the major league roster and a handful of right-handers who have been effective against left-handed relievers in their careers.

Gonzalez turned out to be one of General Manager Mike Rizzo’s most unheralded moves last season. The left-hander joined the Nationals in the majors in June, pitched 35 2/3 innings, striking out 39 batters and posting a 3.03 ERA, holding lefties to a .179 batting average and serving as a mentor to fellow southpaws such as Ross Detwiler.

There was mutual interest between the Nationals and Gonzalez on returning to Washington. The left-handed reliever said earlier this winter that he enjoyed his time here and wanted to return, but was hoping for a multi-year deal. Gonzalez said at least ten teams had shown an interest in him and he was open to hearing from them, but his priority was to stay with the Nationals. Gonzalez couldn’t immediately be reached for comment Friday.

The Nationals have Zach Duke as the lone left-handed reliever on the roster next season, bringing him back on a one-year deal to serve as their long reliever, the role once occupied by Gorzelanny. The Nationals could rely on Duke and veteran Bill Bray, who agreed to a minor league deal after struggling with a back injury while on the Cincinnati Reds last season. Bray has held left-handed hitters to a .218 career average. (The Nationals also signed left-handed reliever Fernando Abad, who pitched for the Houston Astros last season  to a minor league deal last month.)

Nationals Manager Davey Johnson said his preference would be to add second left-hander to the bullpen, but he and Rizzo have said that they would be comfortable with their right-handed relievers against left-handed batters next season. The Nationals have honed in on  free agent left-handed reliever J.P. Howell, who punched up a 3.04 ERA in 50 1/3 innings for the Tampa Bay Rays last season, as their preferred replacement for Sean Burnett.

Right-handers such as Tyler Clippard and Ryan Mattheus have been particularly effective against left-handed hitters. Clippard has held left-handers to a .186 average in his career in large part because of his change-up, while Mattheus, with a power sinker, allowed them to hit only .214 off him. Left-handers hit only .198 off Stammen last season and .208 off Henry Rodriguez.

Gonzalez is now the third Nationals left-handed reliever to opt not to return to Washington next season. Burnett, a free agent, agreed to a two-year, $8-million, deal with the Los Angeles Angels of Anaheim earlier this month but it could be worth $13.25 million over three years with incentives. Tom Gorzelanny, who the Nationals non-tendered but were still interested in bring back with the right deal, reached a two-year, $6-million deal with the Brewers just over a week ago, according to the Milwaukee Journal Sentinel.

The Nationals decided that Burnett wasn’t “a fit financially or terms-wise,” and for the same reasons, didn’t want to tender a contract to Gorzelanny, who likely to made at least the $3 million he earned last year through arbitration. And it may be likely the Nationals were outbid by the Brewers for Gonzalez.