How do I create a proper bevel on narrow, pointy shapes? I find myself running into variations of this problem with increasing frequency, where I have a narrow, curved, pointy shape like the one exemplified below, and I can't figure out how to create a bevel that isn't a mess of overlapping and clipping geometry.



Does the problem just lie in my topology, or am I going about this in entirely the wrong way? 

This is what manually correcting the bevel yielded: It doesn't have the best topology, but it seems to work:


Blend File:
There are multiple bevel modes. In 2.79 If you hit "W" then "B" for the bevel tool, you can switch between them by hitting "M"