Treat asparagus like fresh cut flowers—trim the ends and place them in a jar with 1-2 inches of water. Cover the asparagus with a loose plastic bag and store in the fridge for up to 4-5 days.
You can also wrap the cut ends in moist paper towel and store them in a loose plastic bag if you don't have space for standing the jar. Make sure to refrigerate the asparagus as soon as possible.
Produce that likes to be stored in water: