The Simpsons awaken to the sounds of hammering and buzz saws. They make their way outside, and discover a construction crew working in the lot behind the house. It turns out that the site is the future home of a stamp museum. The Simpsons and their neighbors stage a protest, hoping to stop the project. Their distractions affect the construction workers, and before long the foreman announces he’s shutting down the job. Newsman Kent Brockman announces that the museum will be built on the site of Springfield Cemetery, and the cemetery will be relocated to the lot near the Simpsons’ house. Before long trucks loaded with coffins begin rolling down Evergreen Terrace. When the relocation is complete, Bart and Lisa peer out of Lisa’s bedroom window, which has a direct view of the fog-shrouded tombstones. Bart frightens Lisa by conjuring up visions of flesh-eating zombies. That night Lisa has trouble sleeping. She tells herself she believes in science and reality, but when Snowball II happens by with a human skull stuck on its head, she screams. Horrified Lisa dives into bed with Homer and Marge.

Homer tells Lisa that if she agrees to sleep in her own bed the following evening, he’ll do something special for her, even if it means taking a trip to the stamp museum. A short time later the family heads for the museum, where Lenny is making money by charging museum patrons $20 an axle to park on his front lawn. Inside the museum the family takes in various exhibits; including six-foot recreations of stamps featuring inventors such as Fredrick Ives, Katherine Blodgett, Elisha Gray, and Alexander Graham Bell. Another exhibit features the art of Milton Burkhart, a children’s book illustrator who wrote “The Land of the Wild Beasts.” The Simpsons watch a movie featuring some of Burkhart’s lively creations. That night Lisa reads “The Land of the Wild Beasts.” As a rainstorm rages, Lisa strikes up a conversation with Gravedigger Billy, cousin of Groundskeeper Willie. Frightened of Billy, Lisa climbs into Homer and Marge’s bed and pulls the covers over her head. Marge and Homer decide there’s only one thing left to do: show Lisa that they can sleep in her room without being frightened. Later that night, as they lay in Lisa’s bed, Homer and Marge realize the room really is scary. They return to the safety of their own bedroom. Marge decides the family needs professional help. She turns to a child therapist, who concludes that Lisa has suppressed her childhood fears. The therapist wants to charge the family four thousand dollars for a ten-week program that will return Lisa to normal. Instead Homer grabs a book from the therapist’s desk and runs off. Lisa decides there’s an easier way to conquer her fears: confront them directly.

Lisa decides that if she can spend one night alone in the cemetery, she’ll never be scared again. Wiggum and his men search the area for a grave robber. Lisa panics at the sound of a nearby owl. She stumbles and hits her head against a tombstone. Moments later she loses consciousness. Bart tells Homer and Marge that Lisa went to the cemetery. Concerned, Homer and Marge decide to look for her. Still unconscious, Lisa dreams about the wild beasts from the children’s book. One of them tells Lisa that she’s just a little girl, and it’s perfectly all right for her to get scared from time to time. Lisa realizes he’s right. When Lisa regains consciousness, she tells Marge and Homer she’s going to be fine.