As the film opens, a mysteriously tall stranger is perpetrating a bank robbery. He runs out into an alley, where it is revealed that the thief is an adult midget on stilts-- Ant-Hill Harry, alias Baby Face Finster. He throws the money into a nearby baby carriage, and disguises himself as a baby to evade capture. When the police pass by, he gets out, and the carriage rolls down the hill, smashing into a rock and sending the money flying into Bugs' hole. Bugs is overjoyed to suddenly be showered with money, but Finster is less impressed, and begins working on a scheme to get the money back.
Finster uses his baby disguise to convince Bugs he is an abandoned child, and Bugs takes him in. Finster initially dives for the money, but Bugs (who is unaware of the money's origin) forces him away from it and puts him in a playpen. Finster responds by holding his breath until he turns blue, and a concerned Bugs gives him the money.
Later, Bugs tries to give Finster some milk, but discovers he has escaped from his playpen. Finster almost escapes with the money after whacking Bugs over the head with it, but Bugs takes him back in and puts the money on a high shelf. Finster responds by threatening Bugs with a "toy" pistol, which he fires and leaves Bugs substantially dazed. Bugs then decides to put Finster to bed.
After being tucked in, Finster beats Bugs with a baseball bat when he tries to turn out the lights. After this happens twice, Bugs tests Finster by saying "Click," and is promptly beaten. Finster makes it appear as though he were having a nightmare, so Bugs lets him be.
Bugs goes to turn on the television, but the signal is distorted by a loud buzzing noise. Bugs peers into the bathroom keyhole, and discovers a quite hairy and tattooed Finster shaving. He is surprised, but a TV report comes on at that moment, describing Finster as a bank robber who supposedly held up a bank earlier in the day. Realizing what has been happening all this time, Bugs tracks Finster down and intentionally torments him, culminating with Finster accidentally stabbing himself in the buttocks with a knife and swearing heavily. Bugs spanks Finster, revealing weapons hidden in his clothes.
Later, at the police station, there is a knock at the door. An officer answers, to find a tied up Finster, the stolen money, and a note describing who he is lying on the doorstep. Finster is almost immediately thrown in jail. He objects heavily, but Bugs appears through the window of his cell and says, "Don't be such a crybaby. After all, 99 years isn't forever." Iris out.