Norris will pitch on Wednesday, following Ubaldo Jimenez on Tuesday, with Miguel Gonzalez rounding out the series at Texas on Thursday. Wei-Yin Chen, Sunday's starter, will pitch Friday's home opener vs. the Athletics, and Tillman will follow him.
"We'll give him a couple of work days and see if we can build on [Saturday]," manager Buck Showalter said of Tillman, who pitched into the seventh inning for just the second time since April 11. "He's still not where he's capable of being, but he's getting closer. "
Showalter also alluded to the O's preferring that Norris -- who has been the Orioles' best starter -- avoid facing Oakland. He is 0-2 with a 9.35 ERA in four career games against the A's.
"We have a thing we carry around. We don't base our decisions on it, but it's a tiebreaker -- matchups and different stuff, who might need the rest," Showalter said. "Who would benefit from it, who would not benefit from it. Some guys don't want to [get extra rest]. If you kind of look at history, you'll get a pretty good idea of why we did it this way. There's only one history we couldn't take advantage of. We try to satisfy the needs of the team and the pitchers."
Brittany Ghiroli is a reporter for MLB.com. Read her blog, Britt's Bird Watch, and follow her on Facebook and Twitter @britt_ghiroli. This story was not subject to the approval of Major League Baseball or its clubs.