Pick straight, firm asparagus with moist ends. Choose between thin stems (sweeter, more tender) and thick stems (meatier, stronger flavor). 2. To store: Cut 1 inch off the bottom, stand in a cup with 1-2 inches of water, refrigerate, and loosely cover with plastic for 5-6 days. 3. Signs of bad asparagus: slimy texture or unpleasant smell.