Head Warps when Tilting

I haven't been able to nail down a thread that clears this up, though it looks like it's been addressed a lot.

My puppet's head distorts a lot when I tilt my head to one side or the other. It feels like there isn't a single pivot point, but rather a few. I see a lot of references around this issue that point to handles, but, honestly, I haven't really figured out a clear and specific explanation of handles, though I'm sure there is one.

Martin