In the book “Records Truly Is My Middle Name“, John tells the story of his trip down to Dallas to record a song with the Jefferson Starship. The story ends with John driving around with Paul Kantner, and Kantner handing him a “cigarette” that he warns is pretty strong.
Kantner was telling the truth.
At the time the song “Jane” by the Jefferson Starship was a huge hit, and the mayor of Chicago just happened to be named “Jane”. So John re-wrote the words to the Starship song, and got the producer of the Starship to record him singing it…to the original track by the actual Jefferson Starship.
You can listen to it here.