Big banks have an unexpected message for President-elect Donald Trump: Don't trash the Dodd-Frank Act.

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"We're not asking for wholesale throwing out Dodd-Frank," J.P. Morgan Chase & Co. chief James Dimon said at a financial-services conference this week where he and other big-bank executives spoke, often addressing potential regulatory changes for the first time since the election.

That is a contrast to some in Washington who have called for full repeal of Dodd-Frank, the legislation passed in 2010 that imposed new constraints on banks and created new agencies like the Consumer Financial Protection Bureau. A proposal that would effectively replace Dodd-Frank, by Rep. Jeb Hensarling, the Republican chairman of the House Financial Services Committee, has gained momentum since the election.

The Trump team has talked about dismantling the law, although it has yet to state clearly whether this would involve a repeal of Dodd-Frank. Bank stocks have soared about 20% since the election, partly on the belief President-elect Donald Trump in some way will lighten banks' regulatory load.

While banks favor a paring back of regulation, they tend to think in practical terms, rather than ideologically. And their core message seems to be: Make regulation simpler and less costly, but don't return banking to the Wild West days that preceded the financial crisis.

In many ways that is understandable. Banks have spent half a dozen years and hundreds of millions of dollars to adapt to the new landscape. This has caused them to exit businesses such as proprietary trading, rejig their corporate structures to make them safer and focus more on clients' needs. While tearing up Dodd-Frank would seem to unshackle banks, starting with a new regulatory playbook would upend their new business models and divert management.

One of the biggest concerns for banks is that things don't get worse. "The first thing I would ask for is nothing new, no new rules," Citigroup Inc. finance chief John Gerspach said at the conference. "If you haven't figured out yet how all the existing rules work together, don't put on anything else."

Banks acknowledge benefits to the new rules, noting they have helped improve the way firms manage risks and view their businesses. U.S. bankers have also said that having been forced to hold more capital, and build it quickly after the financial crisis, made their firms far stronger than troubled European peers.

So what would the big banks like to see changed?

Stress Tests -- These annual exercises conducted by the Federal Reserve have become hugely important because they govern the amount of capital banks can return to shareholders, either through buybacks or dividends.

Banks want these to be based more on objective criteria and they want to have more of a view into the testing process and the Fed's decision-making. And they should take less time and money to comply with, bankers say.

Bill Demchak, CEO of PNC Financial Services Group Inc., said his bank could theoretically get all the benefits of the stress-testing process with "60% of the effort." He said that to comply with the tests, "you bring the place to a grinding halt once a year."

The Volcker Rule -- Banks say they aren't eager to get back into the business of speculating on market moves using their own balance sheets. But they want the process around the Volcker Rule to be less burdensome and administered by fewer than five agencies.

Changes in this area could "probably make it easier to make markets" and improve liquidity, likely benefiting investors and other issuers, said Mr. Dimon.

"You have active market-marking in lumber, rebar, chicken, pork, cotton; we need it in financial instruments, it's not different," he said. "I do think a little more liquidity could be good."

Mr. Gerspach said Citigroup would like less paperwork. "We don't want to do proprietary trading," he said. "But I also would love to work with regulators to lessen the burden of proving that we're not engaging in proprietary trading."

Capital and Liquidity -- Banks say there are so many new rules relating to so many areas of their balance sheets that they too often run the risk of working against each other. And it isn't clear when enough capital really is enough.

Wells Fargo chief Timothy Sloan cited differences between rules about how much capital a bank must hold and the amount of liquid assets a firm has to keep on hand. The intersections of these rules, bankers argue, hampers lending.

Bankers would also like more clarity around how much capital is enough for banks. Regulators have applied various capital surcharges to the biggest banks and these can change as regulations evolve.

"It's getting certainty around the ability to have access to your capital return once you've met all the hurdles and whether those hurdles move up or down because of various people's point of view," said Bank of America Corp. chief Brian Moynihan.

J.P. Morgan's Mr. Dimon said that regulators' authority should be "cut back a little bit. It should be more prescriptive in exactly what they're trying to accomplish."

For all that, bankers are taking a wait-and-see stance before making any big changes to their businesses. "I think the difference going into 2017 is that we do have hope," Citigroup's Mr. Gerspach said. "But...we can't build a plan on hope."

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