The songwriting credit goes officially to all members of the band, but the song is published by Bob Dylan's Special Rider Music label, indicating that the main writer is Dylan, who is also the lead singer on the record. This is partially contradicted by George Harrison's account of the song in "The True History of the Traveling Wilburys" documentary:

"Tweeter and The Monkey Man" is sometimes regarded as a playful homage to the songs of Bruce Springsteen, who was often hailed as "the next Dylan" early in his career. The lyrics include the titles of many Springsteen songs, and the song borrows many of Springsteen's themes. The setting of the song itself is New Jersey, Springsteen's home state and the setting for many of Springsteen's own songs. New Jersey locations such as Rahway Prison and Jersey City are mentioned by name. Springsteen song title references include: "Stolen Car", "Mansion On The Hill", "Thunder Road", "State Trooper", "Factory", "The River", and the song made popular by Springsteen but written by Tom Waits, "Jersey Girl". Additionally, "Lion's Den" and "Paradise" are each mentioned and prominently enunciated in the song, each being the title of a Springsteen song released after the Traveling Wilburys album.

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