Some tiredness isn't a sleep problem. It is an unfinished-thinking problem: four unresolved things circling, each one costing a little power to keep in the air.
Rest for that kind looks less like a nap than like writing the four things down and deciding one of them. People often stand up from that lighter than they stood up from an hour on the sofa.
None of which helps on a genuinely short night. Some days you are simply short, and the honest move is smaller ambitions rather than a fight with your own eyelids. Energy is a budget before it is ever a virtue.