Mesh Split/Difference Errors

Hey Guys:

Here's the problem, when I use the mesh difference component between a mesh sphere and another mesh I often see this sort of fraying error. The edges of the mesh have a bunch of triangles coming off of them, instead of a smooth cut.

What's curious is that if I slightly change the size of the sphere the error will sometimes go away. I'm looking for a solution that gives me consistent success. Any ideas?

-Oliver