America, as far back as Prohibition-era and up to today-ish. I'm really very relaxed about when this incident takes place so long as I can make it work.
We have a detective of some sort, either a cop or a PI. He gets too close to something that the bad guys don't want him too close to, as one does. So the Head Bad Guy sends an underling to get our detective out of way, permanently. Our guy is shot in the head from a distance. I know that generally one aims for the chest, but assume the detective moves or the shooter is some hotshot showoff. Whatever works for you. (The only real importance of the bullet to the head is that it gives me a solid excuse to have him wear hats. I like hats. It's not a terribly serious story-idea; I just like to have my facts straight, you know?) In any case, our detective is dead, but not for very long. It's rather important to me (and him) that his head remains, uhm, structually sound. So I'm looking to make sure that whatever the shooter uses, the entrance and exit wounds aren't ginormous. And can be easily covered by a jaunty hat.
So, what's your favorite gun for long-distance shooting with small enter/exit wounds?