This is for covers which convey the emotional sentiment of a song much more powerfully than the original version (as opposed to covers which turn the song on its head and give it an entirely different feeling).

Example the oft covered Do What You Gotta Do (Nina Simone and The Four Tops, have both done versions) original is this - http://www.youtube.com/watch?feature=player_embedded&v=7NSjT27M3M0#!

But the version which does the best job of actually sounding like it's actually sung by a spurned lover is by Meg Baird - http://www.youtube.com/watch?v=1rbTnGbkA9Q&t=5m53s