Video duration: 359 seconds
Global video hits: 261434
A lot of people have covered Lennon's great song; but this is the best cover AFAIK, and far better than her studio version.
From the sadly-departed NYC soundstage show "Sessions at West 54th", and first aired on late at night on American PBS stations (with naughty word and all) early in 2000. Video found via ed2k and probably off of her DVD "Dreaming my Dreams".
Video duration: 152 seconds
Global video hits: 214758
Marianne Faithfull, in Rolling Stones Rock n Roll Circus, 1968! Singing Something Better, obviously anxious but great, a song that they expected to be a hit or sth like that. The video came out only some years ago.