Abraham went 1-1 with a 2.19 ERA across 10 games with the San Antonio Missions. In 12.1 innings he allowed 10 hits, walked five and struck out 17. He had season-ending surgery.

Abraham went 0-0 with a 5.52 ERA across 20 games with the Portland Beavers. In 29.1 innings he allowed 35 hits, 19 walks and struck out 21. He allowed five homers and induced three double play grounders while holding the opposition to a .302 average.

2007

Abraham went 0-0 with a 0.00 ERA over four Missions playoff games. In 3.1 innings he allowed two hits and struck out three.

2006

Paul Abraham went 3-4 with one save and a 3.18 ERA over 43 appearances for the Mobile BayBears. In 65 innings of work he allowed 60 hits, walked 32 and struck out 55. The opposition hit .242 off him. He allowed runs in 16 of his 43 outings, ending his season on the disabled list after pitching on August 19. 2005

Abraham went 2-1 with a 1.07 ERA in 35 games for the Lake Elsinore Storm. In 42 innings he allowed 29 hits while walking ten and striking out 36.

Abraham went 2-1 with a 3.98 ERA in 30 games for the Mobile BayBears. In 40.2 innings he allowed 46 hits, walked 13 and struck out 24.

2004

Abraham was signed by the Padres on June 14, 2004 and pitched in 37 games for Fort Wayne. He went 1-2 with a 2.79 ERA for the Wizards, striking out 49 in 48.1 innings of work while walking 15.