Peeling asparagus can be frustrating. If you lay it flat on a work surface, your knuckles scrape the surface as you peel, and if you lift one end of the spear to make some clearance, the pressure from the peeler sometimes snaps the spear. Instead, try holding the spear by its tip and laying the rest of it on an overturned saucepan. The pan provides knuckle clearance and at the same time supports the spear against breakage.
Try this technique out in Shaved Asparagus Salad with Aged Gouda and Hazelnuts.