(Reuters) — The U.S. Senate has approved a bill tweaking the 2010 Dodd-Frank law’s treatment of insurers, a rare adjustment to the Wall Street reform law that had been sought by the industry.

Senators unanimously agreed on Tuesday to give the U.S. Federal Reserve more authority to tailor its capital requirements for insurance firms such as Prudential Financial and American International Group to reflect the ways their business models differ from banks’.

The move stemmed from a portion of Dodd-Frank that directed the Fed to ensure that large, risky non-bank firms face capital requirements comparable to those placed on banks.

Lawmakers from both parties, including Maine Republican Sen. Susan Collins, who wrote the relevant section of the reform law, said they did not intend for banks and insurers to follow the exact same rules.

“I want strong capital standards but they have to make sense,” Sen. Sherrod Brown, a Democrat from Ohio who introduced the bill with Sen. Collins and Republican Sen. Mike Johanns of Nebraska, said in a statement.

“Applying bank standards to insurers could make the financial system riskier, not safer,” Brown said.

Insurance executives and their state regulators have said insurers are not subject to runs on the business in the way banks are in crises, and they do not hold the same types of assets.

Fed Chair Janet Yellen had told lawmakers her agency recognized the differences between insurers and banks but needed more authority to tailor its rules.

Democrats have long been hesitant to allow even bipartisan changes to the sweeping 2010 law for fear its critics would seize the opportunity to try to revamp large portions of it. The decision on Tuesday could mean other adjustments to Dodd-Frank will be allowed to move forward.

The insurance measure, which gives the Fed flexibility as long as insurers are regulated at the state level, is likely to pass the U.S. House of Representatives, where a group of lawmakers introduced a similar bill.

Congress passed the Dodd-Frank law in response to the economic meltdown that began in 2008. It called for hundreds of new rules, including new oversight of the massive swaps market, mortgages and consumer financial products, and large non-bank financial firms.