The White House is putting finishing touches on several measures in an effort to make progress on curbing gun violence, an issue the president and close aides have found frustratingly intractable, before the race to replace him enters prime time.

According to gun industry insiders and others familiar with the proposals, the changes include requiring an expanded number of small-scale gun sellers to be licensed—and therefore conduct background checks—whenever selling a weapon. This wouldn’t close the so-called gun show loophole, though it has the potential to narrow it.

The administration is also expected to impose tighter rules for reporting guns that get lost or stolen on their way to a buyer.