MINNEAPOLIS — The Minnesota Twins must rebuild their bullpen after losing four key free agents.

With a couple of All-Star closers as the anchors in the back, the Twins are counting on a wide-open competition to produce the quality middle relief they’ll need for postseason and championship contention.

The Twins avoided salary arbitration with a pair of relievers, agreeing to one-year contracts with right-hander Matt Capps for $7.15 million and left-hander Glen Perkins for $700,000 on Tuesday.

Capps, who more than doubled last season’s salary of $3.5 million, came to Minnesota in a trade last July with the Washington Nationals, posting a 2.00 ERA over 27 innings with 16 saves for the Twins. With the expected return of Joe Nathan from reconstructive elbow surgery, the Twins have two established closers at the back end of the bullpen.

Nathan, who is under contract for $11.25 million this season, is coming off the Tommy John ligament replacement procedure that kept him out for all of 2010. General manager Bill Smith said Tuesday that the four-time All-Star righty is throwing off a mound.

“I don’t believe he’s had a single setback in his entire rehab,” Smith said.

If Nathan doesn’t immediately retake the closer role, he can be a setup man while Capps handles the ninth inning.

The other spots are less certain, with Jesse Crain (White Sox), Brian Fuentes (Athletics), Matt Guerrier (Dodgers) and Jon Rauch (Blue Jays) all joining other teams.

Perkins will have a clear opportunity to win a spot, a former starter who has been either injured or in the minors for much of the last two years. Right-handed sidearmer Pat Neshek is also coming off a couple of injury-ruined seasons and is in line for another important role if he can prove he’s back to his old form.

“If we get Glen Perkins and Pat Neshek back, that’s huge,” Smith said.

Jose Mijares, A.J. Burnett, Anthony Slama and Rob Delaney are other strong candidates for spots, with varying levels of success and experience. Anthony Swarzak and Rule 5 draftee Scott Diamond are in the mix, too, as well as a number of non-roster spring invitees. Hard-thrower Jim Hoey, who came in a trade with the Orioles for shortstop J.J. Hardy, is a darkhorse option.

Similar to when the Twins let their top two relievers, Eddie Guardado and LaTroy Hawkins, leave as free agents after the 2003 season, they’re committed to rebuilding from within rather than by signing expensive free agents.

“We’ll have some spirited competition for those bullpen spots,” Smith said.

Left-hander Francisco Liriano, right-hander Kevin Slowey and left fielder Delmon Young also are in arbitration this year. Second baseman Alexi Casilla previously agreed to a one-year, $865,000 contract.

The Twins offered Liriano $3.6 million for 2011 and he asked for $5 million. Slowey was offered $2.3 million and he asked for $3.1 million. Young was offered $4.65 million and he asked for $6.25 million.

Arbitration hearings are scheduled for February, but most cases don’t make it that far. Both sides can continue to negotiate right up to the hearings, and they typically settle right around the midpoint of the two proposals.

“Sometimes you get close. Sometimes you don’t. But we’ll continue,” Smith said. “It’s just a process to determine salary. It doesn’t mean we don’t like them. It doesn’t mean they don’t like us.”

The Twins are also continuing negotiations with free agent Carl Pavano, the veteran right-hander they’re expecting to lead their rotation with Liriano again this season.

“We’re still very optimistic. I think Carl wants to pitch here, and we want him to pitch here,” Smith said. “We’re in the home stretch, and we hope to have something done in the next day or two.”