GLENDALE, Ariz. -- Given his famous competitiveness, it came as absolutely no surprise on Tuesday when Zack Greinke said he would like to start for the Brewers on Opening Day.

Greinke spoke following his much-anticipated, if unofficial, Milwaukee debut, and anyone can check the calendar to see the former Royals ace is on an every-five-day schedule that leads directly to his second consecutive Opening Day start. But anyone -- including Greinke -- can also check the roster and see there are two other pitchers who took the ball in 2010 openers, including Yovani Gallardo, the Brewers' incumbent and All-Star who said last month that he'd like the honor for the second straight year. Shaun Marcum is a Brewer, too, and he started the Blue Jays' 2010 opener.

Greinke realizes that manager Ron Roenicke is in something of a pickle.

"Everyone wants to pitch Opening Day, but whatever is decided, it's not like anyone's going to cry if they don't get it," Greinke said. "I was thinking about it. It's kind of tricky."

Roenicke was relayed that comment following the Brewers' 3-1 win over the White Sox at Camelback Ranch.

"Good answer, Zack," Roenicke said with a smile.

With that, Roenicke went quiet. He isn't ready to reveal his pitching plans for the first week of the Brewers' regular season, though he told reporters earlier in the day to expect something soon.

The skipper hinted in previous days that he would use left-hander Randy Wolf in Game 3 of the season to separate him from the other lefty, Chris Narveson, who will be fifth out of the chute. That leaves Greinke, Gallardo and Marcum to fill Games 1, 2 and 4. The first is the team's March 31 season opener in Cincinnati, but the fourth game is just as big because it's the Brewers home opener. Roenicke made clear he views that as a prestigious assignment.

Still, everybody seems to want Opening Day.

"But that's good," Roenicke said. "If guys are upset about not pitching that opener, that's good. Any time you have guys that want the ball all the time, that's great to have."

So, stay tuned. On Tuesday, the focus was on Greinke, who walked three batters in 1 1/3 innings before exhausting his allotment of pitches in a forgettable, 39-pitch debut. He managed to escape a bases-loaded jam in the first inning with a strikeout of Chicago outfielder Dayan Viciedo, and got help after issuing a one-out walk in the second inning from pitching prospect Donovan Hand.

Greinke conceded he has things to work on, such as commanding a fastball that he couldn't elevate when he wanted to against the White Sox, and perfecting his new curveball grip. The game moved fast, which he said was normal for a first outing of the year. The arm strength was there, which was encouraging.

"It wasn't perfect," he said, "but it felt good coming out. So that's a good sign."

Greinke discussed his outing while wearing a machine that delivered electrical stimulation to the left side of his ribs. Greinke suffered bruises earlier in camp that pushed back one of throwing sessions, and club officials declined to say how he was hurt other than it happened off the field.

"I didn't notice it so much today," Greinke said. "I could take completely off, and it would get better faster. So it's just getting better slower, and it might have me a little bit behind. The last couple of days it's been a lot better."

Would he reveal how he was hurt?

"Nah, [the team] didn't say, so I'm not going to say. Sorry," he said, confirming that it happened away from the field, "and it was stupid."

He was grilled some more about the December trade that brought him to Milwaukee. Greinke was on the market after asking the Royals four times to be dealt, and was quizzed on that process by a gaggle of reporters gathered for only his second media availability this spring.

Greinke answered the questions, then politely said he was ready to move on.

"That will probably be the last question I answer about the past," he said. "That's my goal."

Before setting that ground rule, he said of his trade requests, "I kind of had to play the bad guy in order to do it. It would be nice if that didn't happen, but the way things were in Kansas City, if I just kept on being the sweet person, the fans would have been outraged if I got traded. I kind of had to be the bad guy. It isn't always your No. 1 choice."

He realized he was a fan favorite -- "I don't know why," Greinke said -- and by making his trade requests public, he feels he helped avoid "backlash on the organization."

Greinke doesn't pay attention to media or fan hype, but he has heard the excitement from his new Brewers teammates. That matters to him.

"It's cool when you see that the guys on the team are excited about [his arrival]," he said. "I don't know if it's the case that it really makes a big difference, but from what has been said so far, they think I've made a big difference. That's nice to hear."