Abreu progressed slowly, and (except for four games) did not advance out of Single–A until 2001, compiling an ERA of 4.64 in a full season for the Double–A Greenville Braves.

After that season, he was traded to the San Diego Padres for Rudy Seánez, and then the following spring to the Chicago Cubs for Syketo Anderson, and after 11 appearances, released six weeks later.

He was picked up by the Kansas City Royals, and finished the 2002 season with the Double–A Wichita Wranglers, posting a solid 3.32 ERA.

In 2004, he was released again, had a short stint with the Guerreros de Oaxaca of the Mexican League, and was signed by the Baltimore Orioles in December 2005.

In 2007, the Washington Nationals signed Abreu to a minor league contract, and he started the spring at Triple-A Columbus in an outstanding fashion, pitching 18 innings and allowing only one run.

On February 6, 2009, Abreu signed a minor league contract with an invitation to spring training with the Tampa Bay Rays.

[1] On June 14, Abreu's contract was purchased from the Triple-A Durham Bulls to replace the injured Jason Isringhausen.

On August 6, 2009, Abreu signed a minor league contract to return to the Tampa Bay Rays organization and was assigned to the Triple–A Durham Bulls.

In 2012, Abreu played with the Diablos Rojos del México of the Mexican League, where in 45 games, he went 4–1 with a 3.83 ERA with 15 saves, striking out 38 over 44+2⁄3 innings.