What are some ways to relieve fatigue without sleeping?

Big picture. Real fatigue must be distinguished from boredom (the bane of educators, preachers and good employers), caffeine withdrawal, and dysthymia / depression (have you felt worthless or not wanting to live)? A need to sleep, and caffeine withdrawal, can only be remedied by sleep. Please do not drive while you are tired, and do not try amphetamines to stay awake.