JPMorgan Chase & Co.’s higher offer for Bear Stearns today gave the investment bank control of nearly 40% of its ailing rival, blunting the threat that angry shareholders could scuttle the deal.

The $2.4 billion lifeline to rescue the investment house stands a strong chance of success — assuaging investors unhappy with a $2 per share offer by upping it to $10 apiece. JPMorgan has faced an outcry among Bear Stearns shareholders about the lowball offer, and faced the possibility that rival deals would begin to surface.

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Most analysts said a higher bid was unlikely, but some bondholders have reportedly been buying the stock in order to ensure their right to vote for a deal and prevent a bankruptcy that would wipe them out. Bear Stearns’ shares — which hit $160 last year and still traded near $80 earlier in the month — nearly doubled to $11.25 today.

However, for a company whose market value went from $8.3 billion to about $1 billion in a little more than a week, the revised deal was still not the outcome investors hoped for. It also didn’t help out the 14,000 employees — one-third owners in Bear Stearns — who have seen the value of their stock holdings plummet and still face the potential of massive layoffs.

“Whether you got $2 or you got $10 was the difference between nothing and nothing,” the chief executive of Al Frank Asset Management, which held shares of Bear Stearns, John Buckingham, said. “For an employee whose retirement was 98% wiped out, they had nothing to lose hoping to get more money out of bankruptcy — and that behooved JPMorgan to raise the price.”

There has been outrage since the Federal Reserve tapped JPMorgan to rescue the 85-year-old investment bank in a deal some feel was hastily arranged. The buyout was put together over a weekend, and within a few days the JPMorgan Chief Executive, Jamie Dimon, was trying to rally Bear Stearns executives to his side.

In exchange for the higher-priced offer, Bear Stearns agreed to sell 95 million newly issued shares to JPMorgan. That gave JPMorgan a 39.5% stake, providing an almost certain majority in any shareholder vote.

JPMorgan, the nation’s third-largest commercial bank, also renegotiated the Federal Reserve’s role in the offer. The central bank originally agreed to guarantee $30 billion of Bear Stearns assets, including risky mortgage-backed securities. JPMorgan said it will now take on the first $1 billion of losses, while the Fed backs the rest.

Mr. Dimon, who needs only another 10.5% of shareholders to approve the takeover, appears to have outflanked any other deals. The agreement, filed with regulators last week, prohibits Bear Stearns employees or directors from soliciting any alternative transactions.

“We believe the amended terms are fair to all sides and reflect the value and risks of the Bear Stearns franchise,” Mr. Dimon said in a statement.

Investors agreed with his tactics, sending JPMorgan shares up 58 cents to $45.55.

Bear Stearns shareholders, meanwhile, are expected to vote on the deal within the next few months.

The Fed, along with the Treasury Department, has drawn criticism for bailing out a Wall Street investment bank that many feel have been reckless amid the credit crisis. The higher price for Bear Stearns could be uncomfortable for Fed officials and the Treasury, Secretary Henry Paulson, who played a key role in the rescue effort. The New York Fed declined to comment.

Last week, Mr. Paulson publicly defended the Fed’s actions, noting that shareholders were nearly wiped out at the original $2 per share price and argued that such losses would discourage other companies from counting on government help in the future.

A Treasury spokeswoman, Jennifer Zuccarelli, said in an e-mail that “an orderly transition of Bear Stearns is in the best interest of our financial markets. The updated arrangements between Bear Stearns, JPMorgan, and the Federal Reserve are consistent with that goal.”

JPMorgan’s higher offer — the initial price was $236 million — comes at a jittery time for Washington and Wall Street alike. A total collapse of Bear Stearns would have rippled through the economy, locking up credit even tighter, and torpedoing global stock markets.

The housing collapse and credit crunch spurred record-high home foreclosures and led financial companies to rack up multibillion losses from complex mortgage investments that turned sour. As credit problems spread, financial institutions became increasingly wary of lending, causing businesses and consumers to hunker down.

Bear’s financial troubles began in July, when two hedge funds it managed nearly collapsed from big positions in securities tied to subprime mortgages. The investment house had to bail out the funds and take possession of many of their instruments.

The revised bid dented hopes by retail investors for another offer that would value the company more fairly. There have been reports that a billionaire financier, Joseph Lewis, one of Bear Stearns’ biggest shareholders, and the Chairman and former CEO, James Cayne, would team up for a rival bid.

A Lewis spokesman, Doug McMahon, didn’t return a call today seeking comment. A spokesman for Bear Stearns also did not return calls.

The renegotiated agreement does not eliminate the hurdles to the deal, which is still the target of shareholder lawsuits.

A senior partner at Wolf Popper LLP, Marian Rosner, whose firm was one of many that filed class action lawsuits against Bear Stearns on behalf of employees, said today that “selling for $2 or $10 doesn’t really make a difference.”