PHOENIX -- Each of starting pitcher Edwin Jackson's two at-bats during Friday's 4-1 loss came as a leadoff hitter, meaning he was able to swing away. Jackson grounded out to shortstop twice, almost beating out a slow roller up the middle to start the sixth.

It's a good feeling for pitchers to take one deep on a rare occasion, as Mark Buehrle, Jake Peavy and Jackson can attest, as well as closer Sergio Santos -- in another baseball life. But the White Sox pitchers' role in the Interleague offense, and possibly key to the pitcher staying in a game, is getting down those bunts when asked.

"Getting your bunts down, that keeps you in the ballgame," said Phil Humber, a one-time National League hurler, who starts Sunday's series finale. "I'm sure [manager] Ozzie [Guillen] is going to watch and see who can and can't do it. That's the difference between being taken out in the fifth or seventh innings.

"As a pitcher, if you get up with a guy on first, or first and second, with less than two out, you are going to bunt --that's the bottom line. It's fun to go out there and swing, but we've all been concentrating really on our bunting, because that's what we are going to be asked to do most of the time."

Peavy will likely face Cubs on Wednesday

PHOENIX -- When it comes to the White Sox pitching alignment for this week's BP Cup challenge against the Cubs, manager Ozzie Guillen has nothing to hide.

Jake Peavy will start one of those three night games, with Peavy indicating on Saturday how that start looks as if it will come Wednesday night at U.S. Cellular Field.

"Hopefully, he stays healthy," said Guillen of Peavy. "That's the main thing. Hopefully, he can go out there and not go back and do the same stuff we have been doing all year.

"He has been traveling all over the country just to try to pitch for us. It's hard for this guy. It gets to the point where I feel for him, because I know he went through a lot of difficulty."

Peavy made his latest, and what he hopes will be his final, Minor League rehab start for Triple-A Charlotte this past Thursday. So, Tuesday would be the earliest the right-hander could start.

His strained right groin got through this latest test with high marks, with Peavy having to come off the mound and make a play on a bunt and then cover first on another bunt. He's ready to improve on a 5-2 career mark against the Cubs and then help propel the White Sox toward the top of the American League Central without any more injury interruptions.

"I'm excited to pitch in the Cubs-Sox series and excited to pitch at home in that series," said Peavy, who termed his nine-strikeout rehab start on Thursday as more of a cautionary measure with his recent injury history. "I had a couple games against those guys. They're starting to play good baseball. I've watched some video. I'm excited to get back there and put a big league uniform on and try to help."

Guillen indicated Peavy's return would mean a six-man White Sox rotation at least through the All-Star break.

Konerko's brother and dad hit with foul ball

PHOENIX -- John Danks wasn't the only one who survived a scare regarding a struck baseball making a connection during Saturday's 6-2 victory over the D-backs. Paul Konerko's brother and father were hit with the same foul ball over the White Sox dugout during a seventh-inning Brent Lillibridge at-bat, but the captain reported no serious family injuries.

"My brother stuck his hand in front of my dad, trying to get it, and his thumb is pretty swollen," Konerko said. "And then my dad kind of got it through the hands off the chin. But they are both fine.

"And my mom was talking through the whole thing and didn't see anything," added Konerko with a smile. "When that ball went over the dugout, I almost didn't even want to look up there. I knew that was where they were sitting and I figured my mom wouldn't be paying attention. So, we dodged a bullet. My brother's thumb is black and blue. That's no big deal, compared to what it could have been."

White Sox won't be stealing bases often

PHOENIX -- The White Sox basestealing has been shut down, and not just by the opposing catchers. With his team just 30-for-59 in stolen-base attempts this season, manager Ozzie Guillen made a decision to slow down his baserunners.

"I shut it down a little bit more, because we were giving away outs with no reason," Guillen said. "I want to see how the team functions without the running game. The running game wasn't working. It was killing us."

Juan Pierre, who topped the Major Leagues last year with 68 stolen bases, is just 10-for-19 this season. Pierre pointed out how opposing teams clearly were going to make adjustments and not let him run after watching what he did in 2010.

Dunn to get start in right field on Sunday

PHOENIX -- Right-hander Josh Collmenter starting for Arizona in Sunday's series finale means left-handed slugger Adam Dunn will be in the predominantly left-handed-hitting lineup after missing the first two Interleague contests, aside from a ninth-inning appearance as a pinch-hitter during Saturday's 6-2 victory. Dunn was hitting .294 with two homers and six RBIs in his last six starts, but now has to deal with inactivity at National League ballparks.

"This is something I never thought about," Dunn said. "You don't think about this kind of stuff until it gets here. I don't know what you do.

"It's why I hate Interleague. I hate it. I'm feeling so good again. ... Yeah, that's about right."

With Paul Konerko clearly the White Sox most productive hitter, manager Ozzie Guillen doesn't want to remove him from the lineup. So, Dunn was ready to take his turn in left field in upcoming Interleague games at spacious Coors Field against the Rockies and at Wrigley Field against the Cubs. But he will get his first chance Sunday in right at Chase Field, giving Carlos Quentin a day off.

"We're gambling tomorrow," said Guillen of Dunn's outfield start. "I need to get Adam some at-bats."

"If that's the case, that would be fine," said Dunn, who has not played the outfield since 2009, but has been taking fly balls during batting practice for the past month. "I probably wouldn't be able to run down as much as Juan [Pierre], but if it's hit at me, I can catch it."

White Sox look to improve with runners on

PHOENIX -- Jake Peavy believes better execution of fundamentals in every aspect of the White Sox game will help this team find greater consistency. Manager Ozzie Guillen went even more specific with his area of concern.

"Men on third base and less than two outs," Guillen said. "I don't say concern. That's the one thing that [bothers] me the most. That's killing this ballclub, all the way from the beginning."

The White Sox are hitting a respectable .270 with runners in scoring position and less than two outs entering Saturday's game, but just .226 with runners in scoring position and two outs.

Third to first

• Dayan Viciedo has completed his paper work to become a United States citizen.

• Konerko is batting .446 with six doubles, eight home runs and 18 RBIs in his last 17 games.