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Put your eyeliner pencil in the freezer for 20 minutes before sharpening and it won't break as easily. It will sharpen very well too!
Source: My daughter told me this tip.
By linn from Dartmouth, Nova Scotia
Before sharpening eye pencils or lip pencils, place in freezer to firm up a bit. Less breakage.
I use makeup pencils for eyebrows, eye liner, and lip liner. I was always having trouble when it came time to sharpen them, because no matter how careful I was, the tip would break off.
I started putting the pencils and the sharpeners in the freezer for an hour or two before sharpening, and they will harden just enough to make it easy to do without breaking.