Dempster had a side session on Saturday, and pitching coach Larry Rothschild said that all went well.
"Right now, it's not a real concern," Rothschild said of Dempster.
The right-hander wasn't too concerned.
"I felt good throwing," he said. "I slept kind of funny, and it tightened up on me and I was a little sore. I threw long toss today and a little side [session], and it felt great."
He joked that he didn't like to make the drive to Tucson, and the Cubs have one more trip on Tuesday to face the Colorado Rockies.
"On Wednesday, I'll feel wonderful," Dempster said.
All Wood would offer on Saturday was that he'll be fine. He has a mild strain of his right triceps and was examined on Saturday by team orthopedic specialist Dr. Stephen Gryzlo. He was able to throw on Saturday without any restraints.
"His strength has been good in all the tests the doctors have done and the trainers have done," Rothschild said. "We'll keep proceeding and do what we can as his arm allows us."
Wood can do as much as he can tolerate.
"He's worked hard all winter," Rothschild said. "As you get into the throwing part, things change a little bit. I didn't expect him to go through a spring completely clean. That would've been nice, but that's not to be expected after everything he's been through."
The right-hander underwent arthroscopic surgery on his right shoulder in late August 2005, was able to make four starts last year, then was shut down with a partial tear of his right rotator cuff. Wood is now projected for the bullpen, and he had looked good this spring.
Rothschild said that the problem isn't from overuse.
"I think it's more turning up the velocity and the adrenaline and all that," he said. "As you start to put that kind of intensity on your arm, you're taxing yourself a little bit more, and that's when things show up. We have to get him through this and hopefully build up after this."
Rothschild wasn't sure how much of a setback the injury would be for Wood, and he says he'll take things day by day.
"We're not going to push it to get it sore again, but we'll keep him throwing to tolerance," Rothschild said.
Prior threw 59 pitches in a Minor League intrasquad game on Friday, and he's scheduled to start on Thursday for the Cubs against the San Diego Padres in Peoria. It will be the right-hander's second start and third Cactus League game this spring. In 3 1/3 innings over two games, he's given up seven earned runs on eight hits and five walks.
"The report was that he was better," Piniella said about Prior's outing on Friday.