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Most of the Basement Tapes songs have some funny turns of phrase ("the comic book and me, just us, we caught the bus."), but a couple can be classified as full-on comedy and are absolutely hilarious: a doo-wop parody called "I'm Your Teenage Prayer" and a bit where Dylan and The Banddeliberately slaughter a Mexican ballad.
They turn the Stylistic SuckUp to Eleven on the Ode to Intoxication "Bourbon Street". Bob cheers on a painfully bad trombone solo (probably played by Rick Danko): "Play it pretty now, boys! Sounds MARVELOUS!...A ton of joy! I can't take it no more!"
On The Bootleg Series VI: Live 1964, recorded just as Dylan was trying to break free of the Protest Singer mold, he is very clearly baked to the gills and in a very good mood. For instance, his reaction to an audience member requesting "Mary Had A Little Lamb".
The travails of the narrator of "Just Like Tom Thumb's Blues" get rather amusing, even if you feel sorry for the poor sap. His Screw This, I'm Outta Here! reaction to end the song caps off the tour de force.
Same goes for "Stuck Inside of Mobile With The Memphis Blues Again", except the situations are more surreal. Don't you hate it when you go to send a letter only to find someone stole the post office?
"Foot of Pride", for all its Crapsack World-ness, is hysterically funny.
He looked straight into the sun and said "Revenge is mine!" ...But he drinks, and drinks can be fixed.
Even the swap meets around here are getting pretty corrupt
"Highlands" is a 16-minute rumination on mortality, morality and failure... in the middle of which, Dylan pops into a diner and gets into a bizarre argument with the waitress, who thinks he's a famous painter and refuses to let him go until he draws her. The section ends with Dylan running out without paying and returning to his Serious Philosophizing.