Accidental death (a child getting a hold of one, for example) and suicide are often brought forward as examples of this, alongside murder in a 'heat of the moment' situations.

In fact, I've rarely heard 'predetermined' murder as the primary argument in discussions I've had on the matter (at least over here in Europe). Mostly because murderers who intend to do so with guns will not be deterred by guns being illegal, so it's relatively weak argument.

The key method of reducing violence to other people and reducing death by suicide is to reduce access to means.

Reducing access to guns would help both problems.