If at first you don't succeed … offer more money.

In a second unsolicited bid, United Financial Bancorp Inc. in West Springfield, Mass., announced late Tuesday that it had increased its offer for CNB Financial Corp. in Worcester, Mass., to $10.25 a share, or $23.4 million in cash and stock.

CNB had originally agreed, in April, to sell itself for $8.50 a share to the $2.7 billion-asset Berkshire Hills Bancorp Inc. in Pittsfield. United countered in May with $10 a share, leading Berkshire to raise its offer to $9.23. CNB accepted that offer on Friday, prompting United to try again, by offering an extra quarter per share.

"I was surprised and disappointed," said Richard B. Collins, the president and chief executive officer of the $1.2 billion-asset United. "I hope they will seriously consider our new offer. I can't put myself in their shoes. I can just put my cards on the table and see if they are willing to consider them."

Collins said that, as a sizable target in a nearby market, CNB meshes with his growth plan.

"Strategically it is a good fit," Collins said. "Worcester is about 45 miles to the east in terms of geography. It is out of our existing footprint, but it isn't a leap … and it gives us a presence in one of New England's largest cities."

Charles Valade, the president and CEO of the $300 million-asset CNB, said its board would take United's offer under consideration and would likely make a decision within the next week.

Berkshire did not comment by press time.

Analysts have said CNB would be a good match for either bidder because its six-branch network is contiguous to both. The company has become the target of a bidding war mainly because it is in an area with few other targets.

Mark Fitzgibbon, the head of research at Sandler O'Neill & partners LP, said he does not expect Berkshire to raise its offer again. "If they get it at this price, it is a good deal, and if they don't they get a very good breakup fee."

Valade said the breakup fee for the deal is $970,000.

Fitzgibbon said that he would be surprised if United's unsolicited offer prevailed, and that more than price will affect the CNB board's decision.

"In the banking industry, it is rare that the folks who go hostile end up winning," he said. "Do … [the CNB board members] want to take a deal with someone who has essentially gone hostile, or do they want to go with the people they negotiated a deal with, and who they feel over time offers the most value?"

Collins said: "I just want to be sure they understand our position. It isn't intended to be hostile. … If it were hostile, you run a risk of destroying a transaction."

In its announcement last week, CNB said it chose Berkshire's offer because United's first offer was at a fixed price, while Berkshire's could increase with the price of the company's stock.

Also, United's deal was contingent on its conducting due diligence, which could create uncertainty. Finally, CNB said it sees more risk in United's being able to close the deal and integrate the acquisition.

But Collins said he doesn't buy those reasons, and noted that because United did due diligence on CNB months ago, it would only need two days to update the files.

In the letter United sent to CNB on Tuesday, Collins laid out several reasons why he believes United's is the superior offer. "We believe that the inconvenience of this modest time delay is minimal in comparison to a significantly higher price for the shareholders," the letter said.

Collins said United is no Johnny-come-lately. He said he has been courting CNB for three years, and that he left discussions in February only because he was told CNB's bare-minimum price was $12.75 per share.

"You can imagine our surprise, then, to learn, less than three months later that CNB had entered into a deal valued at $8.50," he wrote in the letter to CNB. "Given the wide disparity between $8.50 and $12.75 it would have been reasonable to expect that CNB's advisors, acting in the best interests of the shareholders, would have recommended that we be brought back to the table even if that meant waiting out whatever period of exclusivity might have been built into any preliminary agreement with Berkshire."

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