Last week’s 2,300-page overhaul of financial regulation could mean that consumers, not just banks, will bear the financial burden of the regulations, Wells Fargo & Co. CEO John Stumpf told Bloomberg.

Stumpf said that he couldn’t guarantee that the bank wouldn’t pass on some of the costs associated with the new regulations.

“We’ll try to tighten our belt and absorb some of the costs of compliance, but some costs may change, and customers might pay for their financial services in new ways,” Stumpf told Bloomberg.

Add Stumpf’s comments to similar comments made earlier this month by CEOs at JPMorgan Chase & Co. and Bank of America Corp., and it seems likely that the new rules will mean new expenses for consumers.

Wells Fargo, which last month ended free checking and added a $5 monthly fee for customers who don’t meet certain conditions, is the largest U.S. branch network and could be setting a precedent for other banks.

“This bank does not intend to sit there and get nailed,” Richard Bove, a banking analyst at Rochdale Securities LLC, told Bloomberg. “Wells Fargo has moved well ahead of the crowd, and everyone will follow.”

Still, Stumpf said he wasn’t sure yet what the actual costs will be for Wells Fargo, because it is still looking for ways to offset expenses and lost revenue. And, he said, despite some shortcomings Congress got many parts of the reform right.

“Too-big-to-fail has been dealt with,” said Stumpf, whose bank holds $1.2 trillion of assets. “Regulators needed a way to understand risk at the top of the house and opine on that risk. They did it in a way that makes a lot of sense.”