I am not sure I believe in more gun control, but here is something I came up with:
1a. The English system--with very, very few exceptions, prohibit semi-automatic rifles and pistols.
1b. If mental issues are present, pass a severe psychological evaluation before purchasing a gun.
2. One of the purposes of a government is to protect its people, and while most people are able to safely own a firearm, not all people are. It is fairly simple to obtain a gun if you have no criminal background.
3. A prohibition on semi-automatic rifles and pistols would help prevent these mass killings, since they are the ones that can cause the most damage. All of the killers were mentally unstable, and many of these instabilities were known before the shooting. Obviously this wouldn't prevent them from taking the gun from someone else, but it would help prevent them from obtaining a gun legally, while the prohibition on the semi-automatics would keep them from taking it.
4. The Bill of Rights does not grant citizens a right to EVERYTHING. There are limits to Free Speech--you can't slander, lie, use fighting/offensive words, make threats, etc. In District of Columbia v. Heller, the Supreme Court ruled that "the right [to bear arms] is not unlimited. It is not a right to keep and carry any weapon whatsoever in any manner whatsoever and for whatever purpose," only weapons that are 'necessary,' as some people see fit, solely for lawful purposes, such as self-defense. These semi-automatic weapons are not.