U.S. regulators worried that banks and brokerage firms remain too dependent on risky types of short-term funding are weighing new rules designed to reduce reliance on parts of what is often called the shadow banking system.

Now the SEC is weighing new funding rules for brokers as well as a limit on leverage similar to those used by the Federal Reserve and other regulators for banks, according to a regulatory document and SEC officials familiar with the matter.

The initiatives are aimed at financing tools such as repurchase agreements, or repos, that were relied on by Bear Stearns Cos. and Lehman Brothers Holdings Inc. until their failures accelerated the 2008 financial crisis. Lehman's bankruptcy provoked criticism of the Securities and Exchange Commission (SEC) for lax oversight of investment banks.