Joe Girardi

New York Yankees manager Joe Girardi (28) stands by the batting cage before an exhibition baseball game against the Detroit Tigers in Tampa, Fla., Tuesday, March 24, 2015. (Kathy Willens | AP)

(Kathy Willens)

KISSIMMEE, Fla. -- Three more down and a week to go.

The Yankees shipped a trio of pitchers out of major league camp Sunday, inching them closer to naming a fifth starter and rounding out their bullpen. Opening Day is April 6, just around the corner.

Scott Baker was released from his minor league contract. Kyle Davies and Bryan Mitchell each were sent to minor league camp.

Davies and Mitchell each are expected to start the seasons with Triple-A Scranton/Wilkes-Barre. It's also conceivable that the team will resign Davies to add rotation depth there.

Demoting Mitchell made it all but clear Adam Warren will earn the last starter's job. Mitchell was already far behind in the competition for the job, which also included Esmil Rogers. Rogers was slated to pitch out of the bullpen for the Yankees against the Astros in Kissimmee, Fla., Sunday.

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Girardi said he didn't want to name his fifth starter yet because he hadn't spoken with the player personally. It's almost unimaginable he'll pick anybody but Warren, who's pitched well this spring.

There appeared to be a chance Baker could earn a long relief role in the Yankees' bullpen, but he was shelled Saturday, opening the door for Chase Whitely to take the job.

Along with the long relief spot, the Yankees are also trying to decide who will take their other open bullpen spot, and who will win the backup catcher competition between Austin Romine and John Ryan Murphy.

Brendan Kuty may be reached at bkuty@njadvancemedia.com. Follow him on Twitter @BrendanKutyNJ. Find NJ.com Yankees on Facebook.