Barring a few institutions that kept their balance sheets healthy and their noses clean during the run-up to the financial crisis, most of America's big banks have spent the past few years struggling to regain their financial footing, salvage the confidence of investors, and return to some sense of normality. For investors, normality means a return to generous dividends and share buybacks.

The Federal Reserve just released the results of its latest round of bank "stress tests." And for some banks, that return to normality is finally at hand. For others, it's back to the balance sheets. Here's a recap of events, along with the two banks expected to increase their dividends the most.

The beneficial kind of stress
At the height of the financial crisis, the entire U.S. banking system seemed on the verge of collapse. Overleveraging, convoluted trading and securitizations, and an ocean of ill-advised subprime lending left a number of major American banks overexposed, undercapitalized, and in danger of bankruptcy. The investment bank Lehman Brothers did, in fact, go bankrupt. Others were saved only with hastily arranged buyouts by more solvent banks and a mountainous infusion of money from the federal government.

As the banks have slowly recapitalized and repaired their balance sheets, the Federal Reserve has periodically run them through tests simulating how they would hold up in the event of another crisis. In this month's test, the worst-case scenario included a 50% decline in the stock market, 13% unemployment, an 8% drop in gross domestic product, low interest rates, and a European market crisis. Under these simulated conditions, banks had to show they could maintain a core, Tier 1 capital ratio above 5% of risk-weighted assets.

The stress-test process is analogous to having a doctor put a patient on a treadmill, wire him up, and then monitor his biological responses as the pace is increased. So how did the "patients" do? 

Run, fat boy, run
 Four out of the 19 banks failed their stress tests, and of those four, the most surprising was Citigroup's (NYSE: C). The too-big-to-fail bank failed its test by a hair, scoring 4.9% out of the needed 5%. For Citigroup shareholders eager for that return to normality, this means that Citigroup won't be able to indulge its shareholders with either share buybacks or increased dividends and will have to go back to the drawing board with the Federal Reserve. Besides Citigroup, Ally Financial, SunTrust, and MetLife also failed their stress tests.

JPMorgan Chase (NYSE: JPM), which did better than most of the too-big-too-fail banks during the financial crisis, came out of the stress tests looking strong. JPMorgan itself said it will return $15 billion in equity to shareholders in the form of share buybacks, and the bank will raise its quarterly dividend to $0.30, pushing its yield up to 2.6%.

And having wisely averted many of the temptations other big American banks fell prey to, Wells Fargo (NYSE: WFC) also came out of the financial crisis in very good shape. As such, The San Francisco-based bank had no problem passing its stress test and has raised its dividend as well, also to 2.6%.

Bank of America (NYSE: BAC), which got wrapped up in epic amounts of mortgages that proceeded to go south -- particularly after some bad acquisitions -- did pass its test but announced even before the results were released that it wouldn't be raising its dividend. Morgan Stanley (NYSE: MS) will also not be raising its dividend; the investment bank is currently trying to buy back 14% more of rival Morgan Stanley Smith Barney and, as such, is squirrelling away its spare capital for that.

Please do not feed the banks
Banks are hungry to raise their dividends or buy back shares -- anything to create shareholder value and get their share prices out of the ditch. But no matter what the dividend yield is, many of these large banks must still be approached with extreme caution.

While passed off by the Federal Reserve and complained about by the banks themselves as stringent, these stress tests were, I think, more of a minimum passing grade to get back out into the real world. Balance sheets are still by no means perfect, and there a lot of mortgages out there ready to go into default, which could potentially undo all the work that's been done to pass the stress tests. Even Morgan Stanley's CEO, James Gorman, said: "All investors should care about is did we pass. A couple of years ago very few banks could have passed."

My personal favorite of the big banks, by far, is Wells Fargo, which really kept its head on straight throughout the 2000s and has a well-deserved reputation for being a steady-Eddie, traditional bank (as least as traditional as big banks come these days). As for all the others, do your due diligence. In that spirit, learn about some delightfully straightforward bank stocks, including one Warren Buffett could have loved in his earlier years, in our free report, "The Stocks Only the Smartest Investors Are Buying." Download your copy while it's still available and the stocks are hot.