Prior to the Brady bill, to buy a gun in the US all you needed to do was go to a store, fill out a yellow form that asks you if you are a felon and if you are mentally ill, and then they hand you a gun. Now at least there is a 3 day waiting period, which means that when you lose your head and want to kill your neighbor you have to wait 3 days to get satisfaction. But maybe,just maybe, you'll cool off over those 3 days and won't kill someone. Also if you are a criminal they have time to check you out.
Actually, that varied greatly by state. The law in Hawaii, for instance, prior to the Brady Act was more restrictive than the Brady Act. Nor has it ever been shown that a significant percentage of gun deaths were from guns purchased within the previous 72 hours.

And that law is why during the Clinton years gun deaths dropped 28 percent. As I stated above the real problem is not the guns but the people and since we seem incapable of properly screening the people, our only solution is to better regulate the guns.
Crime in general dropped during the 90s, as did cigarette smoking and drug addiction. Were all those the result of the Brady Act? I think it's more likely the reduction in gun deaths was linked to the drop in overall crime.