All the more reason, FDIC officials thought, to slow down the dividend payouts and stock buy-backs.

The Fed did have an effort parallel to the stress test to assess these liabilities, and, according to a Fed spokeswoman, eventually included the legal risks in the stress test.

(In February, banks settled robo-signing problems with state attorneys general for $25 billion but remain on the hook for other legal liabilities arising from their mortgage servicing.)

By March 2011, it was clear the FDIC had lost its argument. The stress test was winding up, and most of the big banks would get a green light. The agency made a last stand on one bank: SunTrust, a large regional bank based in Atlanta.

The Fed had determined that SunTrust passed the stress test and could exit TARP. Bair appealed to Tarullo, according to several people familiar with the matter. The objection has not previously been reported.

The FDIC didn't think SunTrust was ready to pay back the government and leave the program. It was one of the last big banks to still have TARP money. It was loaded with high-risk assets, such as interest-only, adjustable-rate mortgages and loans to borrowers with low credit scores.

But the Fed shunted aside Bair's appeal and allowed the bank not only to repay the government but to do so on indulgent terms that the FDIC thought left SunTrust still vulnerable. When it green-lighted SunTrust's exit, the Fed didn't adhere to the 2-for-1 replacement standard regulators had established for healthy banks. The bank issued only $1 billion in new common stock to repay the government's $4.85 billion in preferred stock.

The FDIC had lost again.

Two former Fed officials who held senior posts during the crucial decision-making say they were troubled, believing that SunTrust didn't have enough capital. "I was horrified," says one of the officials.

Since then, investor views have mirrored those of the Fed's critics. In 2011, SunTrust shares tumbled more than 41 percent. The bank has a market value of about half of the value of the assets on its balance sheet -- a sign that investors suspect the bank is overstating the worth of its assets and exaggerating its overall health.

SunTrust and the Fed declined to comment.

WHAT NOW?

Some see allowing dividends and stock repurchases as a confidence-building exercise. The hope is that investors will believe that the Federal Reserve is confident in the banks and will buy bank stocks. Higher share prices mean that banks can sell stock more cheaply if necessary. The regulators' logic seems to have been: Let the banks deplete capital to raise capital.

In the second stress test, "how much was appearance, and how much was reality? The Fed wanted the appearance of strength," says a former senior regulator. "The Fed wanted everyone to see that the banks were profitable, back to normal and back on the road to health. ... And the banks wanted it."