Gomez is arbitration-eligible for the fourth and final time. Axford, Estrada and Narveson are first-time eligibles.
Parra, 30, was a "draft-and-follow" pick of the Brewers in 2001, signed in 2002 and wound up making 74 starts and 98 relief appearances in the Major Leagues from 2007-12. But he never quite lived up to the outstanding potential he teased when he pitched a perfect game in his first Triple-A start in 2007.
Parra's best year was 2008, his first full season in the big leagues, when he was 10-8 with a 4.39 ERA in 32 appearances, 29 starts. His ERA jumped to 6.36 in 2009, when Parra was demoted back to the Minors after being removed from an Interleague loss to the White Sox, and he had a 6.19 ERA as a starter in 2010 before the Brewers bumped Parra to relief.
In that role, Parra thrived, and he entered 2011 pegged as a reliever only to miss the entire season with back and elbow issues. In 2012, Parra returned to make a career-high 62 appearances, pitching to a 3.51 ERA through the end of May, but finished with a 5.06 ERA and walked nine batters in as many September appearances.
"Sometimes a change of scenery can help a player," Brewers general manager Doug Melvin said. "From our standpoint, it was time to move on and see if we can turn the page and find someone else. We have Manny the opportunity here, and he was appreciative of it. There are times you just have to move on. ... We went through a lot with Manny. Manny went through a lot with our club, as well.
"But consistency is what we're looking for. Manny is frustrated, too, as a player. Players always want consistency, too. He still has a very good arm and he has a very good chance of performing well."
Parra thanked the Brewers for giving him an opportunity, but expressed an eagerness to begin anew.
"I'm excited, because I feel like there's been some baggage that is tough to move on from," he said. "Being a starter -- a failed starter, in my opinion -- I feel like no matter what I did, I was always being compared to what kind of a starter I was, and trying to overcome those things. I'm excited to move on and improve and be a better player."
Asked to expound on the concept of "baggage," Parra said that being bounced from the starting rotation always gnawed at him, and now he's trying to "grow up."
"I was never able to let it go," he said. "I just beat myself up a lot. I'm trying to move on from that stuff. I'm really trying to change the way I think."
Melvin suggested that Parra may be best suited to return to a starting role.
"That's just my personal opinion," Melvin said. "He was just inconsistent, and sometimes, in the bullpen, Manny tries to do too much. He has two or three pitches, and sometimes coming out of the bullpen, you have to try to simplify things. He has the repertoire of pitches that, if he throws strikes, he may be better to be a starter."
The Brewers had previously cut ties with four other mainstays of their 2012 bullpen: Kameron Loe, Livan Hernandez, Francisco Rodriguez and Jose Veras.
Melvin said the club has had only preliminary discussions with its four remaining arbitration-eligibles. The sides will continue to talk until Jan. 18, at which time those players still unsigned exchange proposals with the clubs for one-year deals.
Axford and the Brewers discussed a multi-year contract last spring, but Melvin said the sides were focused on a one-year deal for now.
With Parra's dismissal, the Brewers have two openings on their 40-man roster.
"I just keep telling myself I'm a late bloomer," Parra said. "I always have been in my life. I'm 30 years old now, but I'm just going to remain positive and believe that I'm going to keep getting better. What else can you do?"