Well, there's the story of the hagoromo -- it's a mystical feather cloak that a tennin has! One night, a fisherman finds one left hanging on a tree, and he takes it because it's pretty. The tennin it belongs to see him trying to steal it and she gets rea~lly mad at him, but he won't give it back. So he makes her promise him to show him a special dance that only the tennin know about.

She dances for him, and he keeps his promise! And after she takes the hagoromo back she disappears like a mountain hidden in mist.