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04/10/11 6:20 PM ET

Dunn participates in batting practice Sunday

CHICAGO -- Although Adam Dunn missed his fifth straight game after having an appendectomy performed early Wednesday morning in Kansas City, the slugger took batting practice on Sunday morning. Dunn reported nothing really inhibiting him during the swings.

"It was good to get out of solitary confinement and hang out with the general population, you know what I mean?" Dunn said. "I feel better than I did yesterday, which is good.

"Again, the guys that are looking at me are a lot smarter than I am. I just want to be ready when I'm in the lineup, whenever that may be."

Dunn could return some time during the Oakland series, beginning Monday night.

"I wouldn't call it a learning experience," said Dunn with a smile. "I feel like I'm being punished. It's kind of like you are being punished, being grounded, and you don't know what you did. I hope it never, ever happens again."

Cooper likes flexibility of bullpen core

CHICAGO -- From the beginning of Spring Training, White Sox pitching coach Don Cooper stressed one word where his bullpen was concerned: flexibility.

Matt Thornton was anointed as closer at the start of the 2011 campaign. But with Chris Sale, Sergio Santos and Jesse Crain also able to effectively pitch the ninth, even before Thornton's two blown saves, the hard-throwing left-hander wasn't considered an automatic ninth-inning option like New York's Mariano Rivera or Kansas City's Joakim Soria, as examples.

"We didn't have the quote, unquote closer name," said Cooper of his bullpen. "We have more than a few guys who can handle the last three outs.

"I'm also a believer in the bullpen sorts itself out in time. They will be showing us who needs to be pitching as you go."

Cooper always has been fiercely protective of his pitching staff, so his defensive reaction to criticism of the early bullpen flaws was expected. Cooper also was right on the money.

Two games stand as a virtually impossible control group to base a season for a reliever set to make 70-75 appearances. Cooper acknowledged that Will Ohman had a rough finish to Spring Training, so the boos heaped upon him after a pair of bad outings in Cleveland were understandable.

But Ohman has made three straight solid appearances since. Thornton needs to locate his fastball a little better and mix in a few more breaking balls, according to Cooper, but Thornton still is throwing the ball well.

"Right now, if you look at Matt Thornton, are you down on him? I'm not," Cooper said. "Are you down on Sergio Santos? No. Are you down on Chris Sale? No. Are you down on Jesse Crain? No.

"Will Ohman has had two good outings in a row. People can't be judgmental too early. If you had two bad days at work in the real world, should you be fired?"

Cooper toys with short-term six-man rotation

CHICAGO -- Phil Humber gave up just one run over six innings in Saturday's victory over the Rays, apparently earning the right-hander an interim but regular spot as the rotation's fifth starter. Humber would next take the mound on Friday in the series opener against the Angels, if the White Sox chose not to skip him with Thursday's off-day.

But with Jake Peavy also climbing back toward the Major Leagues, what will happen to a still effective Humber when Peavy returns? White Sox pitching coach Don Cooper made it clear on Sunday that Humber would stay with the team as a long reliever and not move to Triple-A Charlotte, where he could start regularly. Spot-starting wouldn't be an issue for Humber, whose arm bounces back quickly even after extended relief work.

A six-man rotation also could come into play involving both Peavy and Humber, according to Cooper.

"Overall, long term? No," Cooper said. "Short term, one time here or there, giving our starters an extra day depending on the schedule with off-days and rainouts, it's certainly something that has popped in my mind.

"Let's just say the first time through we have a lot of games in a row, and maybe we would think about. I like thinking out of the box. Everyone gets an extra day and has a chance to catch your breath. It's a long season, and you want guys sprinting across the finish line, not falling across."

Humber didn't make much use of a cutter he worked on during Spring Training in Saturday's win. He did work ahead in the count, and relied on his changeup and curve.

"He was the story of the game, the way he threw the ball, especially the way [Friday] night's game ended," said White Sox catcher A.J. Pierzynski. "To come out and shut them down the way he did, it was awesome."

Peavy moving up to Triple-A for next start

CHICAGO -- Jake Peavy's next rehab start will take place Wednesday at home for Triple-A Charlotte, with the Knights taking on Durham. Peavy threw 3 2/3 innings and 71 pitches for Double-A Birmingham on Friday in Montgomery, Ala., but remains a ways away from a big league start for the White Sox.

"Three more starts possibly before Jake can even think about being back with his pitch total being where it's at," said White Sox pitching coach Don Cooper of Peavy, who will go somewhere around 80 pitches on Wednesday. "He has come along nicely.

"We knew there might be setbacks, and there were. What I'm hoping now is that there are no more setbacks and it's a continual climb the rest of the year. It will be a shot in the arm to get another quality pitcher on our team."

Peavy was scheduled to be with the team in Chicago at some point on Sunday and will throw a side session under Cooper's guidance on Monday.

"If he's climbing like we are hoping he will climb, to have a climbing Jake Peavy is an exciting thing," Cooper said. "We might have a stronger guy in July, August and September or in the playoffs. That is my long-range hope."

Buehrle, Ramirez receive 2010 awards

CHICAGO -- Mark Buehrle received his 2010 Rawlings Gold Glove and Alexei Ramirez picked up his 2010 Louisville Slugger Silver Slugger Award prior to Sunday's first pitch. It was the first such honor for Ramirez and second straight for Buehrle.

"I don't want it to be just because you win it one year, they keep on handing it to you until you are out of here," Buehrle said. "I still want to go out there each year and try to earn it."

Third to first

• Sunday's 6-1 victory over the Rays was played in just 2 hours, 8 minutes, the White Sox quickest game of the season.

• The White Sox improved to 6-1 in day games and picked up their sixth win two weeks ahead of last season (April 23).

• The White Sox have led in all nine games this season.

• Gavin Floyd has a 2.87 ERA over his last 141 1/3 innings and 22 starts, dating back to 2010.

• Paul Konerko has hit in 10 straight, dating back to Oct. 3, 2010, and has 28 career multihomer games.

Scott Merkin is a reporter for MLB.com. Read his blog, Being Ozzie Guillen, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.