Looks like loosening gun control either lowers the murder rate or has no effect on it.
I say this because as more guns have gotten into the everyday citizen's hands, the death toll has fallen.
I won't make the correlation / causation mistake.
There are definitely more guns.
The murder and non-neglgent homicide rates have been trending down since 1996 or so.
That means that more guns reduces the murder rate.
Something else is driving the rate down and more guns don't affect that rate.
More guns really do cause more murders, but it's insignificant compared to the other factors driving it down. (This one is least likely since the rate of gun ownership has increased so dramatically that if there was any connection between more guns = more murder it would show up and it doesn't.)
And that's it, really.
None of those three scenarios calls for increasing gun control.