Finster, a 35-year-old man who resembles a baby, makes a successful robbery of the Last National Bank by the swift use of stilts, dark clothes, a carriage and baby clothing.
Finster loses his money down Bugs' rabbit hole and gets himself unofficially adopted in order to give it back. Multiple attempts to grab it are interpreted as a baby's typical grabbiness. Finster even pulls and fires a gun but this still does not fully register with Bugs. Finster beats Bugs with a baseball bat; he assumes the baby is having a bad nightmare.
Later, Bugs finds Finster is in the bathroom shaving himself, smoking a cigar, and wearing a tattoo (labeled Maisie, Singapore, 1932). A brief news clip makes the rabbit realize what is going on. He takes the time to torment the man, before trussing him up like a baby (At one point, Finster tries to stab Bugs but stabs himself in the rear. He murmurs inaudible obscenities, causing Bugs to spank him and remove the weapons he had) and leaving him and the money at the police station. Finster does not take it well, throwing a wild tantrum
- On ABC, Cartoon Network, and the syndicated version of the Merrie Melodies show, the part where Finster draws a gun on Bugs and he thinks it is a toy is cut. The cut is not easily visible because the jump cut is to the same layout, though one can tell a cut is present due to the change in audio.
- On ABC, in addition to the aforementioned cut, the part where Bugs, having learned Finster's identity, shakes Finster after catching him trying to get the purse full of money atop the bookshelf, puts Finster in the washing machine after handling the "dirty" money, throws Finster up to the ceiling, and lets him fall flat on his face. The edited version is done in such a way, it looks like Finster just fell off the bookshelf.
- Some syndicated airings of this cartoon on local TV stations merely shorten the part where Babyface Finster is shaken after Bugs catches him trying to get the purse full of money ("How many time have I told you not to play with the dirty money?!").