The agency that regulates the U.S. accounting industry on Tuesday proposed a new standard for public company auditors that would give them more leeway to focus on areas they consider most critical, among other changes.

The new auditing standard, proposed in a unanimous vote by the five members of the Public Company Accounting Oversight Board, came in response to industry complaints that audits of companies’ internal financial controls under the 2002 Sarbanes-Oxley antifraud law are too expensive. It was a companion move to the Securities and Exchange Commission’s proposal last week to ease financial-control rules for smaller public companies.