Then I suggest a relativily easy permit system. The idea is that criminals will be denied permits and then hit them hard for illegal possession when cought. People that already have a permit for a weapon type/class should not even have to deal with a waiting time for their weapon. To be allowed a permit the applicant should need to be able to show that:

1. You are a responsible person that will not missuse your weapon.
(Prove to use that you are NOT a criminal or a nuthead).
2. You Know how to safley operate your weapon.
(So you don't accidentily shoot someone while while cleaning your weapon for instance).
3. Are a good enough shot to not hit an innocent bystander.
(Get yourself to a firing range and get some training and show us the result).

For continued permits the permit possessor should need to prove all three requirements when asked to do so and with some regularity. This seems to be about every five years in my country. Permits are recalled if the permit owner no longer meets the reqirements. Kiss your permit goodby if you become blind for instance (3.)

The law are more complicated then this where I live but I just made up a condensed version that may work for you Americans. We also has to prove that we actually need the weapon we are applying for a licence for.

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Whoever fights monsters should see to it that in the process he doesn't become a monster.
Friedrich Nietzsche