CHICAGO -- The only absolute certainty to come from Jake Peavy's second bullpen session, thrown at U.S. Cellular Field prior to Wednesday's game with the A's, is ...

Well, there's now a little less uncertainty about the right-hander and his overall preparedness to get on the mound.

"Everything went well in the bullpen," said White Sox pitching coach Don Cooper. "We got a really good workout in. He feels pretty good about it. I feel pretty good about it, too. The best I can tell you is we'll see how he feels [Thursday] and continue to map out a plan for him to go out and pitch."

"I'm just getting prepared to go out there and play," Peavy said. "I went about as hard as we could go there for 50 to 60 pitches, and I felt good. I'm just trying to get that endurance back up to where I can go out and compete."

Peavy's two side sessions have come during rehab stint No. 2 for the somewhat snake-bitten veteran. He made four Minor League starts for Triple-A Charlotte to test a partially torn tendon in his right ankle, suffered while with San Diego, and build up his arm strength and feel for his pitches. That Major League express was derailed upon taking a Wes Timmons' line drive off of his pitching elbow on Aug. 24.

That impact caused soreness and inflammation -- although no structural damage -- and it set Peavy back a few weeks. He threw an approximately 60-pitch bullpen session on Sunday and then used Wednesday's session as more of a game-simulated setup.

Between each set of pitches, Peavy would sit down in the White Sox bullpen as if it was between innings.

"We wanted that because, obviously, that's what you do in a game," said Peavy. "The next step to get in a game is to simulate the actions and mentality-wise."

"He did everything -- full stretch, full windup, [threw] all his pitches [and] went over hitters," Cooper said. "We talked about many, many hitters he could be facing in the next two weeks. We're not limiting it to the Angels or Seattle Mariners. But those are the guys we spoke about -- played the game out there and had fun doing it."

Much of the decision on the next step for Peavy will come from how he feels on Thursday, when he comes in during the team's off-day to get treatment before making the trip with the White Sox to Anaheim. The options would be to have Peavy throw another side session, probably Saturday or Sunday at Angel Stadium, or give him a start, most likely Tuesday night at Safeco Field in Carlos Torres' rotation spot.

"[Hopefully] we will make the decision one way or another," Peavy said. "It's whether I'll have another sideline or throw me into the fire."

"All I know is that it went pretty good and we'll continue to map out a plan for him," Cooper said. "We're not going to give you a date. He's not going to give you one."

Reports from Peavy on his elbow ran pretty much the same as Sunday. He's not 100 percent, but neither is any other player at this point of the season. Peavy's goal simply is to get out on the mound and help the White Sox before the 2009 campaign comes to a close.

But both Cooper and Peavy are in agreement that trying to enhance the team's fleeting playoff hopes will not be used to push Peavy if he's not completely ready.

"I wanted to play from the first day I came over here, but obviously I knew I had to be smart," Peavy said. "I think we were on track to make that New York start [at Yankee Stadium, the weekend of Aug. 28] that we all had hoped for.

"Who knows how much I would have helped? Simply because I know I'm not the pitcher I know I'm going to be in the future right now, because of all the setbacks and injuries I've had to overcome. I would be motivated to get out there in the race, out of the race, no matter what. I would love to pitch. If that happens this year, I certainly would be happy. If it doesn't, we will see what happens."