Asparagus is best cooked the day it's purchased, but it can be kept in the refrigerator for up to five days in one of the following ways: Wrap the bottoms of the stalks in a damp paper towel, and place in a paper bag; store in crisper. Or stand the bundled stalks in a bowl with about an inch of water.
Although many people believe that thinner asparagus spears are more tender than thicker ones, thick spears are actually just as tender. If the asparagus stems are tough, remove the outer layer with a vegetable peeler.