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07/04/11 11:23 PM ET

Danks progressing with oblique recovery

CHICAGO -- Having never experienced the injury before, White Sox starter John Danks had no idea what to expect after straining his right oblique on June 25.

Now just more than a week later, Danks said he is happy with how his recovery has progressed and -- after playing long toss over the weekend and taking Monday off -- plans to throw a bullpen side session "within the next couple of days."

"Honestly, it feels good," Danks said. "It's getting better every day. Certain baseball motions still kind of get me, but that's part of it. We're not that far into it yet."

Danks' current stint on the DL will last up until the All-Star break, but the left-hander doesn't necessarily plan on using those extra four days just to rest. Though the Triple-A All-Star break runs from July 11-13, Danks said his plan as of now is to get a rehab start out of the way during the break.

"In a perfect world, I'd do it over the break," Danks said. "Then I'd be ready to come back the first time through the rotation. It's all dependent on how I feel obviously, but that's the goal right now."

Dunn looks to get going with Interleague over

CHICAGO -- Potential reasons for Adam Dunn's struggles have been debated at length this year. Among the ideas tossed around have been facing new pitchers in the switch to the American League, his move to designated hitter and simply playing for a big-market team with high expectations like the White Sox.

With Interleague Play now over -- his struggles continued against the National League -- Dunn was back at DH and batting third for Monday's series opener against the Royals, but he was hoping he took something away from Interleague Play.

"The second [at-bat], I don't know what it was, something felt actually normal for the first time in a while," Dunn said after Sunday's game. "Hopefully, that will carry over to [Monday] and we can kind of get it going."

While Dunn couldn't describe exactly what he meant, he said he felt a noticeable difference in his last three at-bats Sunday against the Cubs.

Leading off the top of the fourth inning Monday, Dunn lined a base hit into right field, marking just his second hit off a left-handed pitcher in 55 tries this season. In response to a loud ovation from the fans at U.S. Cellular Field, Dunn played along by tipping his helmet to the crowd as he stood on first base.

After the mock ovation in the fourth, Dunn received a legitimate ovation in the eighth inning, when he blasted a two-run homer to temporarily put the White Sox ahead, 4-3. He was also at the plate in the bottom of the ninth after the Royals tied it at 4, but catcher A.J. Pierzynski scored the winning run on a balk call with Dunn ahead in the count 1-0.

Dunn was on the field well before any of his teammates, taking another live batting practice session against left-hander Garrett Johnson and right-hander Stephen Sauer, two Minor League pitchers who have been doing rehab work with the White Sox since their road series in Colorado. Though there haven't been any noticeable differences in his stats since the sessions started last week, manager Ozzie Guillen hopes the feeling Dunn had on Sunday is a sign he could be turning the corner.

"We're going to continue to do that, as long as he wants to, to try to get him better," Guillen said. "We've been doing it a few times, but it hasn't worked. Hopefully, today it gets something in his mind, he thinks positive and hopefully he gets something out of this and hopefully he starts hitting."

Lillibridge gets nod in left field vs. Royals

CHICAGO -- Looking to give Juan Pierre a day off, White Sox manager Ozzie Guillen called upon Brent Lillibridge to start Monday's game in left field, marking Lillibridge's first start since June 25.

Lillibridge hit just .212 in the month of June and struck out 18 times while recording a new career high for at-bats in a single month with 52. Despite not appearing in the starting lineup, Lillibridge was able to record at least one at-bat in five of the team's last seven games after entering as a pinch-hitter, pinch-runner or defensive substitution.

"It was helpful getting even just a pinch-hit at-bat because of the National League rules," Lillibridge said. "So I'm ready, I feel comfortable out there. My swing feels good, so I'll just do what I do, swing at good pitches, be balanced and see what that results in."

Guillen has said all year that, although he considers Lillibridge to be the team's best defensive outfielder, he is still unsure if the utility man is ready to contribute as an everyday player. Lillibridge went 2-for-4 with a pair of singles Monday and stole two bases.

Lillibridge's 113 at-bats this season are already more than his previous career high of 98, and Monday was the 57th game for the 27-year-old, who played in a career-high 64 last season. After posting slugging percentages of .560 and .657 in April and May, respectively, it dropped off to .346 in June.

White Sox searching for success in division

CHICAGO -- From 1997-2008, the White Sox posted a winning record against their division for 12 straight seasons. Sitting at 7-11 in divisional games so far this year, they are trying to avoid what would be their third straight losing season against their American League Central foes.

Having played a league-low 18 divisional games until this point, the White Sox have plenty of time to improve their divisional record. Monday's win against the Royals marked the first of 19 straight games against AL Central teams for the White Sox, including a seven-game homestand before the All-Star break against the Royals and Twins.

"It's a big week at home," first baseman Paul Konerko said. "We have to make sure we don't get caught looking ahead. It's probably a good thing we're playing Kansas City and the Twins. ... Having a divisional team in front of you, you know you have to dig in."

The Royals were the only divisional opponent that the White Sox posted a winning record (10-8) against last season, while they have been dominated in recent years by the Twins, going just 11-29 since 2008, including 0-4 this year.

By winning the series opener Monday, the White Sox evened their record at 43-43 and took a step in the right direction toward reaching Konerko's goal for the team going into the break.

"I think a short-term goal is to be above .500 come Sunday," he said. "I mean better would be great, but that should be kind of a goal, and we'll take that into the break and move on."

Third to first

• Adam Dunn's eighth-inning home run was the 382nd of his career, moving him past Joe DiMaggio for 72nd on the all-time list.

• Monday was the fifth time the White Sox have won this season when trailing after seven innings. They are now 5-33 in those situations, while the Royals fell to 20-6 when leading after seven.

• It was announced Monday afternoon that Paul Konerko led the 2011 American League All-Star Game Final Vote sponsored by Sprint after the first day of voting. Voting continues until 3 p.m. CT on Thursday.

• As part of the Fourth of July commemoration, members of the United States Armed Forces stood at each of the nine positions prior to the first inning as the White Sox took the field and thanked them with a handshake and autograph.

Paul Casella is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.