Sharpen a pencil with a knife.
Have a very sharp knife.  Hold the pencil in one hand and the knife in the other. Place the knife onto the pencil where you want to narrow the pencil, above where the pencil point will be.  Move the knife away from you and towards the point. The angle of the knife should be shallow such that it removes a layer of material as the knife is moved. Rotate the pencil a small amount and repeat the material removal until the pencil point it formed.