CHICAGO -- Don't look for quotes from Ken Williams about continued help he might be seeking for his American League Central leaders via the waiver wire during the month of August.

That talk would be somewhat disrespectful to the players currently on the roster who have brought the 2012 team to their lofty perch. But that respect factor doesn't preclude the White Sox general manager from keeping more than an eye open for that one extra piece that could push the team to greater postseason glory.

"It's a mistake to sit in this chair and feel like there's not one more move to make," said Williams. "So, I will constantly challenge our staff to find that one more move, that difference maker.

"Sometimes the difference maker isn't an impact player. Sometimes it's a fit here or there. That's the best way I can put it. We are always looking for that one more move."

Waiver wire decisions present an interesting game within the game as to whether a team should claim a player as a potential block or let him possibly fall to another contender. But with the White Sox pretty well set across the diamond, don't look for an Alex Rios-type of talent or contract to be added like he was on Aug. 10, 2009.

"This is a different situation because we are where we are and we don't have a lot of positions where if you claim somebody they're going to come in and play," Williams said. "And then once you start talking about those possibilities you take away, I think, from your club and the people that have brought you to this point.

"So I'd rather not get into it and talk about it. We have what we have right here and we'll fight together with these guys. You certainly don't want to allow teams with better records than you to capitalize on players. The fortunate thing when you're on top of your division is you're darn near last in the claiming order. So it helps me from doing something stupid."

Williams admitted to monetary constraints making potential additions more challenging, as he was able to get money included in deals for Kevin Youkilis and Brett Myers. But he won't use it as an excuse.

"We are where we are. You haven't heard any crying from us," Williams said. "We're grinding it out, just like we're asking the players to grind it out. It's up to us to do the same thing.

"You first identify the possibilities that are out there and try to be as resourceful as you can to make it happen. Some times you're more successful than others."

Beckham hopes hits start falling down the stretch

CHICAGO -- By Gordon Beckham's estimation, August and September should be his best months with the bat.

"People say it all the time: You have two good months, two mediocre months and two bad months," Beckham said. "I've had two bad months. July was not good for me and April was not good for me. May and June were pretty good, but I don't think that's as good as I could be.

"So if that's the case, then I've got hopefully two big months ahead. That would be a great end to this season."

Beckham produced a .153 average in April and a .188 average in July. He hit .261 in May and .276 in June. He also has been continuously frustrated by hard-hit balls not finding a little piece of grass in the outfield to help his cause.

His offensive approach could be more consistent, by Beckham's own admission. But Beckham has put himself in better position to get hits this season.

"I make good contact and I really don't feel like I've had a lot of luck. I really don't," Beckham said. "People get bloop hits and I've gotten mine. I want the ones that I've hit hard to land.

"Really, I feel like I've hit a lot better than .230. I really do. I feel like I've hit the ball well and I've hit a hard .230, if that's possible. I'm getting taught something again. You know what, I think it can happen these next two months, the hits are going to start falling for me."

Playoff push won't change mindset

CHICAGO -- As the 58-game push to the postseason begins for the White Sox, they don't plan on changing the one-day-at-a-time philosophy that has brought them to this point.

"Just take it day by day, try to win the first game of every series, which obviously is a tone-setter for the series and just grind it out like they always have," White Sox general manager Ken Williams said. "The work hasn't changed. So the approach need not change. Let's just keep grinding away and see where we end up when it's all said and done."

"We like coming to the park and enjoy being here," White Sox second baseman Gordon Beckham said. "I don't know if I've been here when we've been in this spot this late. We've always kind of had some what-ifs, but it seems like we are on the right track here. So, for three seasons it wasn't like this. Now it feels like we've got a good chance to win this thing."

Williams: Liriano the right pitcher to reach goal

CHICAGO -- There were other pitchers on the market that the White Sox could have pursued before trading for Francisco Liriano. But according to general manager Ken Williams, Liriano made the best sense to help them find success in the playoffs and not just get to the playoffs.

"While there might be some other guys out there who were available, I just felt that Liriano's one that all he really has to do is be in the strike zone on a more consistent basis," Williams said. "[White Sox pitching coach Don Cooper] and I have been through this drill before. There were some very immediate and obvious things that we felt could get him in that zone a little bit more and that's all it takes, and I think he can be an impact guy.

"Now you put him into a situation where he's in a roll and we're in the playoffs, he can shut somebody down and he can shut anybody down if he's right. We're [going] after the big prize and not just to get in to say, 'Ooh, we've been to the playoffs.' That's never been our goal."

During trade talks, Williams made it clear very early on to other teams that he wasn't about to mess with the chemistry on the field.

"You don't get into overhauling something that's working," Williams said.

Third to first

• The White Sox adjusted their rotation to have Chris Sale start Monday and Jake Peavy start Tuesday. Peavy was given the extra day after throwing eight innings Wednesday. Sale will be working on nine days between starts.

• Right-handed pitcher Chris Devenski was sent to Houston as the player to be named in the Brett Myers trade from July 21.

• Dewayne Wise, who produced one of the most famous catches in White Sox history to take a ninth-inning homer away from Gabe Kapler during Mark Buehrle's perfect game on July 23, 2009, has rejoined the White Sox via a Minor League deal. He will report to Triple-A Charlotte.

"We feel he needs some at-bats because he hasn't played in a while," Williams said. "But we feel that at some point he can be part of the equation and help us on the bench."

• A.J. Pierzynski has homered in three straight games for the first time since May 14-18, 2005, when he homered in four straight.

• The White Sox are hitting .321 over their last 12 home games and have outscored opponents 84-42 during that time.

• White Sox pitchers have limited the opposition to a .133 average with runners in scoring position over the last 10 games.