The Philadelphia-based rock group Nazz recorded a parody-of-sorts called "Loosen Up", which appeared on Nazz III.
The 1990 song "Do The Brown Nose" by The Dead Milkmen, from their album Metaphysical Graffiti, is a parody of "Tighten Up", with a similar riff and spoken-word element, where "the brown nose" is not a dance but a synonym for being obsequious.