Banks with less than $250 billion in assets would be exempt from company-run stress tests under two separate proposals from the Federal Deposit Insurance Corp. and the Office of the Comptroller of the Currency.

Companies that would still be subject to those stress tests would have more flexibility under the proposals, which follow up on Congress' approval of a package making several tweaks to the Dodd-Frank Act. Those companies would generally have to conduct those stress tests every two years, rather than annually. The stress tests would also no longer include an adverse scenario, which would narrow down the scenarios banks have to model from three to two.

The Federal Reserve recently proposed other changes that would ease company-run stress-testing requirements for bank holding companies with less than $250 billion in assets, among other things.

All three regulators are taking public comments on their proposals.