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Skeleton algorithms with minimal artifacts

I've seen a couple simple algorithms for deriving the 'skeleton' of a shape (known as a 'fiber' in some image processing texts). Example: http://felix.abecassis.me/2011/09/opencv-morphological-skeleton/

But many exhibit artifacts, small side-threads or similar. You'll see the small diverging lines in the B at the link above. That's very common. Felix's page above is very cool, and the code does what it is supposed to do, so no complaints there. I'm just looking for a function that would minimize this, even at the expense of runtime or coding effort.

Any ideas?