[5] After beginning the 2006 season at Class A-Advanced Brevard County, he was promoted to Double-A Huntsville in August and selected to participate in that year's Arizona Fall League.

[7] Parra attended spring training with the Brewers in 2007 where he allowed no runs or hits while striking out 3 batters in 3+1⁄3 innings over 4 relief appearances.

[4][6] He was promoted to the Triple-A Nashville Sounds in mid-June to replace ace pitcher Yovani Gallardo who had been called up to Milwaukee.

[4] Parra made his first career Triple-A start on June 20—a 3–0 loss in which he allowed 2 runs on 7 hits and 4 walks while striking out 6 batters in 6 innings.

[3] On June 6 of that year, Parra became the 52nd major league pitcher to strike out four batters in an inning, doing so against the St. Louis Cardinals.

[15] Problems with his back and the necessary surgical removal of a bone spur in his throwing elbow resulting in him missing the entire 2011 season.

In a year where he filled in for the high expectations of Sean Marshall, he shined, going 2–3 with a 3.33 ERA and 16 holds, striking out 56 in 46 innings (57 games).

[3] On February 22, 2016, Parra signed a minor league contract with the Chicago Cubs that included incentives potentially bringing the total value of the deal to US$2.7 million if he made the 40-man roster.

[19] Despite a strong showing in spring training, he was released by the Cubs and resigned to a new minor league contract on the same day on March 29.

[20] On January 27, 2017, he was signed to a minor league contract and pitched out of the bullpen on 11 occasions for Chicago's Triple-A Iowa Cubs.

[6] On July 31, 2017, Parra signed with the Bridgeport Bluefish of the independent Atlantic League where he played for the remainder of the season.

Though Parra was selected by the Long Island Ducks in the Bridgeport Bluefish dispersal draft,[21] he later signed a minor league deal with the San Francisco Giants on February 27, 2018.

[22] He made 45 relief outings for the Triple-A Sacramento River Cats, recording a 4.28 ERA with 53 strikeouts across 54+2⁄3 innings pitched.