Beefheart and his Magic Band invested a lot in the video for this song, where they perform it the desert. It was supposed to bring the niche band into the living rooms of the masses, but they were quickly deflated when MTV deemed it "too weird" to play.
Those who saw the video did so either on syndicated music video shows like Night Flight, or on David Letterman's show. When Letterman had Beefheart on, he played the video and asked him what "Ice Cream for Crow" means. Beefheart's reply made no sense, but he said it with a conviction that left you believing it made sense to him. A rough transcription: "Ray gun, jelly beans, rope trick, he's a bad actor. What it has to do is black and white at a raven, vanilla ice cream."
Regarding the video, he declared, "I don't want my MTV if they don't want my video," referring to MTV's ubiquitous "I want my MTV" slogan.