OK, I was asked elsewhere for suggestions. Here -- some (I think) sane limits to gun ownership. I could meet these criteria -- anyone much flakier than me probably shouldn't have a gun.
1. Require that civilians pass the same standard of testing that police are required to pass before being allowed to carry.
2. Require that they retest annually.
3. Require that they carry insurance to mitigate any misuse of their gun.
4. Require that they show proof of safe storage -- ownership of a gun safe, at a bare minimum.
5. Require that they pass some basic mental competency test in addition to a competency test -- it needn't take longer than the driving test in which you actually drive the damn car.
6. Require that three persons who are themselves licensed (under the terms above) gun owners, vouch for them as persons of good character.
7. Require that they pass a background check at least as thorough as the one I have to pass to get a job.
... that's a start. I could write an equally long passage on the ways in which I'd like to expand gun rights -- people passing all the tests listed above should be permitted unlimited concealed carry similar to that granted an air marshal, for example, including on airplanes and in other "gun free" zones. License the NRA to perform training to pass the tests; I've known a few NRA instructors over the years, and they're excellent teachers. Perform outreach into at-risk communities to encourage weapons adoption; there are plenty of women out there who plainly should be armed. And so on ...
The purpose is to reduce gun deaths. I refuse to believe that we are, as a society, incapable of filtering people who should be carrying weapons, to the increased safety of us all, from people who shouldn't be -- to the increased safety of us all.