Jindal stands out from the pack on this issue. Former Texas Governor Rick Perry, one of Jindal’s rivals for the GOP nod, said that Thursday’s shooting ought to inspire looser gun laws: “I believe that, with all my heart, that if you have the citizens who are well trained, and particularly in these places that are considered to be gun-free zones, that we can stop that type of activity, or stop it before there's as many people that are impacted as what we saw in Lafayette.” Other Republicans haven’t offered much comment. (Donald Trump, for what it’s worth, says the shooting “has nothing to do with guns.”)

As Jindal noted, Louisiana only implemented automatic reporting of mental-health information to NICS a couple years ago. Even as the national gun-control legislation after the Newtown massacre foundered, Jindal—who enjoys an A-plus rating from the NRA—successfully pushed to overturn a Louisiana law that blocked mental-health reporting to NICS. It’s intriguing to imagine Jindal pushing to his party’s left on gun politics. There simply isn’t much room left to the right, and besides, the NRA has been notably more open to mental-health-focused restrictions than to other types of gun regulation. To paraphrase, the group argues that guns don’t kill people; the mentally ill sometimes do. That means the position that Jindal is staking out isn’t at all radical, even though it’s to Perry’s left.

In theory, federal law has long barred persons who are adjudicated to be mentally ill, or involuntarily committed to a mental institution, from acquiring firearms. In practice, reporting is pretty shoddy—many states simply have no mechanism for or don’t bother to send information to the national database, where it’s used for the background checks that determine whether someone is eligible to buy a gun. Activists say reporting has generally improved in the last few years.

It’s also not clear that, even if the loopholes were closed, reporting of this sort would actually make a difference. John Houser, the Lafayette shooter, is said to have bought the gun he used legally in Alabama in 2014. (Background-check systems have a variety of loopholes and delays, and a failure of some variety allowed Charleston shooter Dylann Roof to purchase a gun.) Some reports suggested that he had been involuntarily committed to a mental hospital in 2008. On Monday, however, the Georgia judge in that case said there had been no involuntary commitment. The judge ordered Houser’s apprehension and evaluation at a mental hospital, but if Houser was released after that evaluation, or voluntarily extended his stay without a court order, he would not have been barred from purchasing a firearm under the law.

Many mass shootings have involved people who wouldn’t have been stopped by stricter laws. That includes those whose names are run through the database without any flags—including James Holmes, the Aurora, Colorado, shooter; Jared Loughner, who shot Representative Gabrielle Giffords and others in Arizona; and now possibly Houser—and those who receive guns from family members or as gifts, including Newtown shooter Adam Lanza.