Sometimes we pastelists need a sharp point or edge on a pastel. My little home-made tool works great, costs very little.
Buy a strip of drywall sanding screen sandpaper, available at Home Depot, Lowes, local hardware stores. It's about 5x11 inches, and comes in different grits. The finer grit is better. The cost is around $3.00.
Shape it over a small plastic container (without its lid), and secure on the sides of the container with duct tape or masking tape. The screen is rather stiff, and takes some effort to bend over the edges of the container, but what a great tool. I use it to quickly sharpen pastels to a point, even the harder NuPastels. Or, to eliminate too much waste of pastel, I run the flat end of pastel over the screen, creating an edge on the rounded bottom.
The grated pastel sifts down into the container, keeping dust and mess to a minimum.