How do I sharpen my eyeliner pencils when it keeps breaking in the sharpener?

I normally don't use eyeliner, but since I got it done at a makeover it looked really good. I bought some pencils and a sharpener which has 2 sizes in one. One size small for eyeliners and th other size bigger for eyeshadow. Well, the soft part of the pencil ALWAYS breaks off inside the sharpener! How can I sharpen the darn things?