Wall Street banks will escape billions of dollars in additional collateral costs after U.S. regulators softened a rule that would have made their derivatives activities much more expensive.

Two agencies approved a final rule on Thursday that will govern how much money financial firms must set aside in derivatives deals. A key change from recent draft versions of the rule—and the focus of months of debate among regulators—cut in half what the companies must post in transactions between their own divisions.

A version proposed last year called for both sides to post collateral when two affiliates of the same firm deal with one another, such as a U.S.-insured bank trading swaps with a U.K. brokerage. The final rule requires that only the brokerage post, cutting collateral demands by tens of billions of dollars across the banking industry. Those costs would still be significantly higher than the collateral they currently set aside.