The group trying to take Dell Inc. (DELL) private is pressing the company to change how it counts shareholder votes to improve the odds of their buyout winning approval, and has offered to increase its bid by less than 1% as an incentive.

Michael Dell and private-equity firm Silver Lake have proposed that abstentions, which currently count as "nos," instead don't count at all in the tally on their buyout bid for the company.

Dell's special committee says it is evaluating the offer, which calls for raising the bid by 10 cents to $13.75, as well as changing the rules on the voting.

Dell postponed--for the second time--a shareholder vote that had been scheduled for Wednesday on the previous $24.4 billion bid to Aug. 2. The meeting was delayed last week after the buyout offer didn't appear to garner enough shareholder support to succeed.

Dell shares were down 0.6% at $12.80 in early trading.

The new offer sets up a game of chicken between company and the buyout group. While both have pressed to see the deal get done, the special committee has wanted to see an ample price bump to win over shareholders, while the buyout group had earlier messaged no bump was forthcoming.

Now, the buyout group is offering a bit more money, but only in exchange for a quick answer-- by 6 p.m. Wednesday--and the proposed vote change designed to help secure passage.

Midmorning Wednesday, the buyout group said about 27% of eligible Dell votes hadn't voted, a bit more than the 23% at which people familiar with the matter pegged the figure last week, when the vote was pulled.

"The will of the majority of the unaffiliated shares voting on the transaction should not be thwarted by an unfair standard that counts unaffiliated shares not voting as "no" votes," the group said in a statement.

Meanwhile, a banker for working with the buyout group, Mark Shafir, co-head of mergers and acquisitions at Citigroup Inc. (C), said on CNBC that the $13.75 was the best and final offer but also hinted that the 6 p.m. deadline for a response for the company might not stick. He said the buyout group was "taking under advisement" changing that deadline.

The board is motivated to complete a deal and avoid a proxy fight to replace directors, which investor Carl Icahn has threatened as he has criticized the buyout deal. But the board also doesn't want to face ire from shareholders by changing the rules along the way. And it isn't clear if the new 10 cent bump would win over shareholders.

Dell's special committee put in place the current voting rules, which also prohibit Mr. Dell's votes from being counted, as a way to limit Mr. Dell's influence over voting on the buyout. He is founder, chairman, CEO and Dell's largest shareholder.

Any changes to those rules are bound to be controversial, and the special committee had worried that such moves could prompt lawsuits from shareholders after the deal, people familiar with the group's thinking have said.

Still, the buyout group has made clear it would only offer more money if it were to see a change in voting rules that would make the bid more likely to succeed, these people said.

Shareholders have been pressing the group to boost the offer, which some have criticized as too chintzy since it was announced in early February.

Richard Pzena, head of Pzena Investment Management LLC, the No. 20 shareholder in Dell as of the most recent data available, criticized the revised offer Wednesday and the board's handling of the situation.

"I can't believe 10 cents is worth changing the terms," Mr. Pzena said Wednesday. "Obviously [Mr. Dell] can't win so he is trying to change the rules."

Under the buyout agreement with the company, the 16% stake held by Mr. Dell and his affiliates can't vote, meaning the buyout group needs at least 42% of outstanding shareholders to vote in the affirmative.

The buyout group on Wednesday called the new offer its "best and final"-- language it hadn't used earlier.

"This is our best and final proposal," said a letter the group wrote to Dell's special committee. "There is simply no rational basis for shares that are not voted to count as votes against the merger agreement for purposes of the unaffiliated stockholder vote."

Mr. Icahn, Dell's second-largest shareholder behind Mr. Dell, has repeatedly criticized the bid, saying the proposal undervalues Dell's shares.

A representative for Mr. Icahn wasn't immediately available for comment.

--David Benoit contributed to this article

Write to Sharon Terlep at sharon.terlep@wsj.com

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