Bank of America and Citigroup stood out for all the wrong reasons in Monday’s market meltdown. Shares of the two banks led the decline amid new doubts about the quality of the assets buried on their balance sheets.

Investors now believe that Bank of America’s net worth is only about a third of what the bank claims; for Citigroup the figure is less than half.

Any time shares of a financial company such as Bank of America or Citigroup plunge it’s particularly worrying. Both are among the roughly 40 U.S. institutions considered too big to fail. The Dodd-Frank Act, adopted in response to the financial convulsions of 2008, was supposed to ensure that taxpayers never have to rescue one of these banks again.

It would be wonderful if Dodd-Frank’s architecture, not even fully in place, was never tested. And maybe it never will be. The U.S. banking industry is in better shape today than three years ago: Banks hold more capital, have more assets that can be quickly converted into cash and are less dependent on the skittish money markets for short-term funding.

Citigroup and Bank of America shares recovered somewhat on Tuesday, but their plummeting prices the day before should still serve as a wakeup call. Because of Europe’s unremitting debt problems and signs that the U.S. is slipping into a new recession, regulators need to more quickly put in place all the tools Dodd-Frank mandated for coping with the next big banking failure.

Dodd-Frank required banks to draw up so-called living wills ― which describe how a failing bank could wind down its business and avoid dragging down other companies. In theory, this should mean a bank would sell pieces of its business, places others into bankruptcy and closes remaining operations. But regulators have put a deadline for writing living-will guidelines on hold while they coordinate with overseas regulators. Former Federal Deposit Insurance Corp. Chairman Sheila Bair wanted the rules for drafting living wills in place by the end of August. That seems appropriate.

Dodd-Frank also required that regulators set up an orderly resolution authority. This authority, established this month, in combination with living wills, would provide a controlled setting for disassembling a large bank. The authority, among other things, lets the FDIC use its money to pay creditors or counterparties of a failing bank so that they, too, don’t collapse in a chain reaction.

In reality, no one knows how any of this would work with companies as vast as Bank of America and Citigroup. Even when markets are stable, the list of potential buyers for Bank of America’s $2 trillion in assets ― or any other major bank’s ― is short. The list would be shorter still in times of crisis, when bank failures tend to occur. Plus, a sale of part of a company like Bank of America to another big bank would do more to concentrate financial assets. The U.S.’s 10 biggest banks already hold roughly three-fourths of the nation’s banking assets, up from about half in 2002.

All the more reason regulators also need to push back against the banking industry’s entreaties to not increase capital requirements too much. Big banks may eventually be required to hold capital equal to as much as 10 percent of assets. When it comes to bank capital, more is almost always better; the level now under discussion at the Federal Reserve probably isn’t high enough.

In an ideal world, Bank of America would go to the stock markets to raise more capital. Capital gives a bank the ability to absorb losses, and Bank of America has had its share. The bank reported an $8.8 billion loss in the second quarter, mostly related to its 2008 acquisition of subprime lender Countrywide Financial. Investors believe more losses are inevitable from those dubious mortgages.

Speculation that Bank of America will raise capital is certainly among the reasons the shares have plunged. Investors are worried that new stock will be sold, diluting their existing holdings. They may have to take their lumps, but if fresh capital is needed there may be no alternative.

One more thing federal regulators should do: Maintain a hard stand against any increases in dividends by weak banks for the foreseeable future. Dividends drain money that can be used to shore up capital and make a bank sounder. At a time when some pundits are declaring the too-big-to-fail problem unresolved, it behooves regulators to do what they can to prove them wrong.

Editorial, Bloomberg