Both manager Joe Torre and general manager Brian Cashman said that Sturtze would need more than one rehab game, though it is unclear whether two will be enough.
"Let's see where he is after two [rehab appearances]," Cashman said.
"Whatever they want is fine," said Sturtze. "I'm ready to get going. I just want to get healthy and be back out there pitching."
Sturtze is eligible to come off the DL on Monday, though he would probably pitch in rehab games on Saturday and Monday, making it unlikely that he would return to the Yankees before next Wednesday. Torre said that Sturtze will remain in the bullpen instead of the rotation, even though Jaret Wright will miss the next four-to-six weeks with a shoulder injury.
"[Sturtze is] really valuable where we have him," Torre said. "He's had so much success doing what he does."
When he returns, the Yankees will have to decide which reliever to unload to make room, though that could mean letting one of their pitchers go from the 40-man roster. None of the team's relievers has Minor League options, so they will either have to trade one of them or designate one of them for assignment and place them through waivers.
"It's obviously something I'll have to deal with," said Cashman, who has yet to explore potential trade options. "I just don't have to deal with it today."
Torre even floated the idea of keeping 13 pitchers on the roster, though that scenario is unlikely.
"We have to figure it out," Torre said. "If the concern is that we don't want to lose anybody, we may go with 13."
Second opinion: Wright will fly to Southern California on Monday to visit with orthopedic surgeon Dr. Lewis Yocum, who is the Angels' medical director.
Yocum, who performed both of Wright's shoulder surgeries in 2000 and 2001, will examine Wright and look at the MRIs taken of his right shoulder on Sunday. The visit was requested by Wright, who left his start on Saturday with pain in his shoulder and was diagnosed on Sunday with inflammation and some torn scar tissue.
"He knows [Wright], so it makes sense," Cashman said. "We support it 100 percent."
The Yankees are treating Wright conservatively, but surgery is not out of the question down the line.
Dandy Andy: Andy Phillips had the time of his life on Sunday, homering in his first big-league start. Tuesday, as he walked into the clubhouse, he found out that he would get another crack at the starting lineup.
Phillips started at first base and batted eighth, taking Tino Martinez's place in the lineup. Jason Giambi was the Yankees' DH, batting sixth.
Torre cited Martinez's lack of success against Angels starter Bartolo Colon as a reason for the move, as Martinez is hitless in 15 at-bats against the right-hander in his career.
"[Phillips] likes to hit the fastball, and Colon's got a good one," Torre said. "Tino hasn't had a lot of success against Colon."
Phillips said he's not looking ahead during his time with the club, preferring instead to take things on a day-to-day basis.
"I'm excited about the opportunity," he said. "I don't ask any questions whatsoever. I don't make those decisions, I just go out there and do the best that I can. My approach is that when I see my name in the lineup, that's as far as I'll take it. I'll go out, have fun and play as hard as I can, then let every other day to take care of itself."
Martinez may be back in the lineup on Wednesday against lefty Jarrod Washburn, as he is 4-for-6 with two home runs against the southpaw. Should Torre opt to keep Phillips in the lineup, it would likely mean a seat on the bench for Giambi, who is just 6-for-26 (.231) against Washburn.
Giambi struggling: Giambi entered Tuesday's game with just one hit in his last 16 at-bats, carrying a .218 batting average with him against the Angels.
Giambi went 0-for-8 in the three-game series against Texas over the weekend, and he has just five hits in his last 29 at-bats.
"The last three or four games went down a little, but when you don't have a lot of at-bats, it happens," Giambi said of his low average. "I had a rough series against Texas. They pitched me tough. It's a long season. I'll just keep going up there and hacking."
Torre didn't seem concerned about Giambi's stats, saying that as long as the effort was there, he couldn't complain.
"We judge it on the quality of at-bats more than what the numbers are," Torre said. "I think he's fine. I sense every once in a while that he's getting frustrated with himself that he's not doing more. He's working hard, and that's really all we can ask of him."
With just 55 at-bats under his belt, Giambi isn't ready to declare his season a lost one.
"Early on, I try to go more by my at-bats than I do my average," he said. "I know if I have good ingredients, the results will come."
Soda star: Alex Rodriguez will join with Angels outfielder Vladimir Guerrero as spokesmen for Pepsi, and the two will star in two national TV commercials for the soft drink.
A-Rod and Guerrero, winners of the last two AL MVP awards, will headline Pepsi's big summer promotion, "Go Pro," with other top athletes.
On deck: The Yankees and Angels will play the second game of their three-game set on Wednesday, when Mike Mussina takes on Jarrod Washburn.