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Parker said he felt fine afterward, and the plan is for him to throw live batting practice on Thursday. He plans to appear in a game before the end of the Cactus League season but added that he has no timeline or expectation about being ready by Opening Day.
"Expectation is not really in my vocabulary anymore," Parker said. "I'm just going to go day to day, be in tune and see how I feel. I'll just give what I've got that day and not try to reach. ...
"What's important to me is to finish this season healthy, not really start it. I'd like to be as healthy as I am right now when I finish the season."
That hasn't happened lately for the 27-year-old Parker. The second Tommy John surgery on his right elbow kept him out for the entire 2014 season. And during a rehab assignment in the Minors last May, Parker fractured a bone in that same elbow while making a pitch. That injury led to another round of surgery.
Parker cautiously has been trying to make his way back ever since. On Sunday, he stuck to a mixture of fastballs and changeups and said he'll begin to add breaking pitches a little later in the spring.
Parker had his first Tommy John surgery in 2010, while he was in the D-backs' Minor League system. He came to the A's as part of the Dec. 9, 2011, trade that sent Trevor Cahill to Arizona.
Parker has enjoyed two healthy Major League seasons with the A's, in 2012 and '13, although secondary elbow problems began to crop up during Oakland's five-game loss to the Tigers in a 2013 American League Division Series. And here he is trying to make it through another comeback.
"I've been about as solid as I could be," Parker said of his rehab. "I put my heart into it, but mentally I kind of separated myself. I was able to check out for a little bit and maintain what I was doing, what the goal was at the end of the tunnel. I think that's what kept me going. Mentally, there may have been days when I checked out, but my heart has always been there."
Barry M. Bloom is a national reporter for MLB.com and writes an MLBlog, Boomskie on Baseball. Follow @boomskie on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.