"Brewers right-hander Zack Greinke will not be rushing back into the rotation, even though he is anxious to contribute after being acquired from Kansas City in a huge off-season trade.

Greinke made his second rehab start Sunday, pitching for the Class AAA Nashville Sounds against Omaha. He was on a pitch limit and threw 54 pitches, allowing three hits and two earned runs in 2 2/3 innings in the game played in Nashville.

Greinke surrendered both runs in the third inning as the Sounds lost to Omaha, 7-3. Former Brewers right-hander Jeff Suppan gained the victory for the Storm Chasers.

"He's going to go one more (rehab start), and if he's not where he needs to be it could be two more," Brewers manager Ron Roenicke said.

Greinke is expected to be able to increase his pitch limit to 75 in his third rehab start, also scheduled with Nashville on Friday against Albuquerque.

In his first rehab start last week he went three scoreless innings with Class A Brevard County. He allowed just an infield hit and struck out four batters while making 35 pitches.

Roenicke was asked if Greinke had pressed to get back with the Brewers earlier.

"Not anymore," Roenicke said with a smile. "He was. To bring back Zack a week earlier or five days earlier and really not have his arm strength, it makes no sense to me. We need this guy for the long haul.

"When he's back here, I want him to be solid for the rest of the season, hopefully getting us into the playoffs. That's when I want him good."

If all goes according to plan, Greinke could pitch in the Brewers' road series against the Atlanta Braves in the first week of May, with a possible return on May 4."