The Federal Reserve significantly scaled back the size of the capital hole facing some of the nation's biggest banks shortly before concluding its stress tests, following two weeks of intense bargaining.

In addition, according to bank and government officials, the Fed used a different measurement of bank-capital levels than analysts and investors had been expecting, resulting in much smaller capital deficits.

The overall reaction to the stress tests, announced Thursday, has been generally positive. But the haggling between the government and the banks shows the sometimes-tense nature of the negotiations that occurred before the final results were made public.

Government officials defended their handling of the stress tests, saying they were responsive to industry feedback while maintaining the tests' rigor.

When the Fed last month informed banks of its preliminary stress-test findings, executives at corporations including Bank of America Corp. , Citigroup Inc. and Wells Fargo & Co. were furious with what they viewed as the Fed's exaggerated capital holes. A senior executive at one bank fumed that the Fed's initial estimate was "mind-numbingly" large. Bank of America was "shocked" when it saw its initial figure, which was more than $50 billion, according to a person familiar with the negotiations.