WASHINGTON (AP) — The Federal Reserve has given the OK to 32 of the 35 biggest banks in the U.S. to raise their dividends and buy back shares, judging their financial foundations sturdy enough to withstand a major economic downturn.

Announcing the results of the second round of its annual stress tests, the Fed also approved the plans of Wall Street powerhouses Goldman Sachs and Morgan Stanley, but on condition they keep their total dividend payouts and stock buybacks at current levels. The new tax law that took effect in January helped tip the two banks' capital reserves below required levels under the hypothetical stress, the Fed said. It was pegged as a one-time impact of the tax law.

The Fed rejected outright the capital plan of the U.S. holding company of Germany's Deutsche Bank, citing weaknesses in its assumptions for forecasting revenues and losses.

State Street Corp. gained Fed approval on condition it improve its analysis of hypothetical lending risks with other big banks.

The yearly check-up tests the banks to determine if their current plans for paying out capital to shareholders would still allow them to keep lending if hit by another financial crisis and severe recession.

The Fed said it applied its toughest-ever "severely adverse" scenario for the economy in this year's tests to see how the banks would fare.

All the banks have at least $50 billion in assets.

After the results were made public, several big banks quickly announced they were boosting their dividends and would increase the amount of stock they plan to buy back this year.

JPMorgan Chase raised its quarterly dividend to 80 cents a share, up from 56 cents a share. The company also announced a plan to repurchase $20.7 billion in stock this upcoming cycle. Wells Fargo raised its dividend to 43 cents a share from 39 cents a share, and announced $24.7 billion in stock repurchases. American Express said its new dividend would be 39 cents a share, up from 35 cents, and it would repurchase $3.4 billion in new stock.

The latest test results "demonstrate that the largest banks have strong capital levels, and after making their approved capital distributions, would retain their ability to lend even in a severe recession," Vice Chair Randal Quarles, who is the Fed's top bank supervisor, said in a statement.

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AP Business Writer Ken Sweet in New York contributed to this report.