CLEVELAND -- Jesse Crain is set to throw a full bullpen session on Wednesday, and if his strained left oblique passes this next test, he'll embark on a Minor League rehab assignment Friday to Triple-A Charlotte.

Crain played catch on Tuesday after throwing another bullpen Monday. The most encouraging sign for the right-handed reliever is the lack of pain during the recovery process following the throwing sessions.

"The first few times I kind of threw, I was kind of sore, like I aggravated it," said Crain, who was placed on the disabled list retroactive to April 21. "Yesterday, I pushed it. I feel it when I throw off the mound, but it's more fighting through the scar tissue and getting it loosened up again and having it recover and feel even better the next time it gets better.

"So Wednesday is my big 'pen, my last 'pen. And I'll try to go as hard as I can 'pen-wise, and go on Friday and Sunday."

That Charlotte trip could return Crain to Chicago on Monday for the start of the two-game Detroit series.

"I felt better every day, and today was the best I felt so far," Crain said. "That's good because I threw a big 'pen yesterday."

Reed happy with current role, hopes to close

CLEVELAND -- The move of Chris Sale from the starting rotation to White Sox closer also seems to have put Addison Reed's big league dream temporarily on hold.

Reed told MLB.com as far back as the start of 2012 that he always had his sights set more on becoming Trevor Hoffman as opposed to Greg Maddux. But with the 23-year-old Sale scheduled to regularly anchor the ninth, the 23-year-old Reed figures to remain in his current setup role and might not get a chance to supplant Sale if he stays in the bullpen.

That change doesn't bother the low-key Reed, who never bought into the closer of the future commentary as much as simply trying to find a productive place on the White Sox staff.

"I'm just going with the flow. Whatever they want me to do, I'm going to do," said Reed, whose 13th straight scoreless appearance to start a season during Tuesday's 5-3 victory over the Indians in 10 innings broke Sergio Santos' franchise rookie record of 12 set in 2010. "As long as I'm going out and pitching, I'll be happy. It doesn't bother me at all."

Career save No. 1 for Reed came Saturday at Comerica Park, when he stranded the tying run at third and winning run at second by knocking out Austin Jackson via a 97-mph fastball. Reed picked up his second save in Tuesday's win, extending his scoreless innings streak to 10, and lowering opponents' average against him to .143 to go with his 14 strikeouts and just three walks.

Even if he never received another save opportunity, though, Reed won't be disappointed or complain.

"As long as I'm pitching, I'll be happy," Reed said. "I'm going to go out there and do my best, no matter what role."

"He's still going to be used in crucial situations late in the game," said Ventura of Reed, who would be next in line to close behind Sale. "I know that."

With Reed's electric stuff and four pitches placing him upon numerous Top 100 prospects lists coming into the season, some have suggested Reed could go from late-inning relief to starter. The only 11 starts of Reed's career came in 2010 for San Diego State, when he finished 8-2 with a 2.50 ERA, two complete games and 90 strikeouts over 79 1/3 innings.

Although he didn't completely shoot down the notion, Reed certainly seems to like this current career path.

"It's up to them, but I'm happy in the bullpen; let's just put it that way," said a smiling Reed. "I think we have a great group of arms.

"They are all awesome. With Chris, all it does is strengthen it. It doesn't hurt to have lefties in the 'pen, especially in the [American League] Central with mainly left-handed-hitting lineups. That's huge."

Stults' solid work earns more starts

CLEVELAND -- Eric Stults' six strong innings in Monday night's White Sox loss to the Indians have earned him at least another start. But after Jake Peavy pitches Wednesday in Cleveland and Gavin Floyd takes the mound Friday at home against the Royals, the White Sox have not yet set their rotation.

"You could go Stults after that or [Philip] Humber just because of the way it works out," said White Sox manager Robin Ventura of his Saturday/Sunday starting alignment. Both Stults and Humber pitched during Monday's doubleheader. "I don't know which one we are going with first, but it's going to be one of those two.

"[Stults] is going to be throwing those games. He's going to be the fifth starter for right now. And it can change at any time, as we found out."

Ventura confident Sale will adapt to change

CLEVELAND -- Robin Ventura got new closer Chris Sale into a game Tuesday night, bringing him in with two runners on and nobody out in the eighth inning to protect a 3-0 lead. The idea was to have Sale work two innings, but he allowed both inherited runners to score and blew the save in a game the White Sox eventually won, 5-3, in 10 innings.

But Ventura has no doubt Sale will be able to handle the change, even if his heart remains with starting.

"It's like in talking to him, mentally, he's ready to do it," Ventura said before the contest. "He wants to be a starter, that's for sure, but I don't expect him to go out there ...

"He's a mature kid baseball-wise for how young he is. Just the way he acts and does things, the way he views his job and as far as the way he looks at his teammates. So I don't see that being a problem."

As for starting eventually returning to Sale's job description after the 2012 season, Ventura reiterated Tuesday that nothing is out of the question.

"Really, there was everything brought up. So it's all still out there," Ventura said. "I think it's trying to figure out what's going on for him and his future as far as trying to protect him the best we can."

Third to first

• After starting both games of Monday's doubleheader, Kosuke Fukudome expressed to Japanese reporters that he would like to get more consistent at-bats to help sharpen his offensive game. Manager Robin Ventura understands and appreciates Fukudome's desire, although he might not be able to immediately accommodate him.

"It's the right attitude. I like guys that want to play," Ventura said. "It doesn't always work out that way. But I like guys that are wanting to play and willing to play. That's always good, but as far as the role that he has, it's more the fourth outfielder."

• Gordon Beckham returned to the second spot in the White Sox batting order Tuesday, finishing 1-for-4 with a walk in the team's 5-3, 10-inning victory. Ventura liked the way he has looked recently at the plate.

"We haven't had much out of that spot," Ventura said pregame. "So just the way he's swinging and doing things, we'll see what he can do there."

• Paul Konerko has 160 career RBIs against Cleveland, the most by any active player.

• The White Sox are 3-6 in a stretch of 15 straight games against the American League Central.