How do I keep from breaking charcoal pencil leads when I sharpen them with a knife? I'm fairly good at sharpening graphite pencils with a knife using the technique in the answer in What is the proper way to sharpen a pencil? 

But I'm always breaking the points when I try to sharpen charcoal pencils. 

How to release the point from the wood when sharpening with a knife without breaking it?

What techniques can I use to sharpen charcoal pencils without breaking the points?
Sandpaper. 

Really, imho the best way to sharpen charcoal pencils is by using sandpaper (100 grit). Works really, really well and the result is perfect.