Rodriguez pitched in Tuesday's Cactus League game against the Rockies and struck out the side. He has four strikeouts in two scoreless innings as he bids for the second lefty role in the bullpen alongside Howell.
Competing with Rodriguez are Daniel Coulombe, Adam Liberatore and Ryan Buchter.
Also in the game, Joe Wieland threw two hitless innings, and Pedro Baez and David Aardsma pitched scoreless innings. Dustin McGowan allowed a run on two hits and has been scored upon in both outings.
The offensive hero for the Dodgers was Scott Schebler, who homered in the bottom of the eighth inning to tie the score. Defensively, second baseman Darwin Barney stole a hit with a diving stop, and the Dodgers turned three double plays.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.