Additionally, the Twins non-tendered reliever Lester Oliveros, but they signed him to a Minor League contract for the 2013 season. Oliveros, who underwent Tommy John surgery in late August, was assigned to Triple-A Rochester.
It's Butera and Duensing's first year of arbitration, while it's Burton's third and final year of arbitration.
Major League Baseball's deadline was Friday for teams to offer contracts for the 2013 season for any arbitration-eligible players. Any players who were not tendered a contract before the deadline became free agents.
Of the three Minnesota players tendered contracts, Butera was the lone non-tender candidate for the Twins, as Burton and Duensing figure to be valuable members of the bullpen next season.
It was a tough decision for the Twins, as Butera is currently third on the club's depth chart at catcher behind Joe Mauer and Ryan Doumit.
Butera has also seen plenty of action in the Majors the last three seasons, combining to play in 184 games, including a career-high 93 in 2011.
The Twins like Butera's defense behind the plate, but he's struggled at the plate in the Majors. The backstop is just a career .183 hitter with five homers and 21 doubles in 487 at-bats.
So the Twins had to weigh Butera's offensive and defensive skills and decided it was worth bringing him back next season. He made $480,000 last season and is expected to be getting a slight raise via arbitration.
Last year, Butera didn't crack the Opening Day roster, but he was called up a month into the season and remained on the big league roster the rest of the way. He hit .198 with one homer and six doubles in 111 at-bats.
Twins manager Ron Gardenhire has expressed his affinity for carrying three catchers on the roster, which likely figured into Butera getting tendered a contract.
The Twins do have a few catching prospects on the way, including Chris Herrmann, who had a solid season offensively at Double-A New Britain and was a September callup.
Last year, the Twins had four players eligible for arbitration -- Alexi Casilla and left-handers Glen Perkins, Francisco Liriano and Jose Mijares. Of that group, only Mijares was non-tendered, and he ended up signing with the Royals as a free agent before ultimately being picked up off waivers in August by the eventual World Series champion Giants.