Wilbur reads about Henry Tyler, a well-known building contractor, planning to build an eight-story apartment house, and sees an opportunity for a contract and architectural job. He knows Tyler used to go to college with Addison, and heads to Addison's house. Addison agrees to recommend Wilbur, but conditioned on being permitted to photograph Ed in a suit and pants for a newspaper competition. Ed, eavesdropping, is indignant at being an object of ridicule. When Wilbur returns to the stable he finds Ed has barricaded himself in.
Wilbur gets in through a window that Ed had not blocked. They argue: Wilbur saying it is only a bit of fun and he needs it if he is to land the contract; Ed thinking it is undignified and threatening to run off to the zoo. Wilbur tries to cushion things by offering suggestions to Carol and Kay on how to make the costume more dignified. But that evening he finds Ed packed up and ready to run away. He tells Wilbur what a dignified family of heroes he comes from, and he does not want to destroy the family pride with a ridiculous photograph. Wilbur is moved and now considers Ed's feelings more. He says he will ask Addison to get another horse but Addison is not sympathetic. Wilbur tries to introduce himself to Tyler at the pool over lunch, but it ends in disaster.
Then Wilbur discovers that Ed has been spinning him a big yarn about his dignified family. Furious, he punishes Ed by having him pose for the photograph in the costume. But Ed's feelings are deeply hurt, and now he does run away to the zoo. He goes to the zebra pen and takes advantage of wet paint on the railings to disguise himself as one. The keepers are a bit skeptical as Ed is too big to be a zebra, but they eventually let him into the pen. Meanwhile, Wilbur finds Ed's note saying that he has run away to the zoo, and heads off to find him.
A group of boy scouts are being shown the zebras. One scout, Tommy, is dubious about the "big zebra" because it has no stripes on its tail. For his part, Ed is indignant at the scoutmaster's claim that zebras are smarter than horses. After Tommy's group moves on, Tommy moves in to investigate. Ed protests to Tommy that horses are smarter than zebras. When Tommy tells his scoutmaster that the "big zebra" talked to him, Wilbur knows he found Ed. He apologizes to Ed and promises he will never let anyone make fun of him again. Ed agrees to come home.
Later, Ed tells Wilbur that there was a phone call from Tyler. He is willing to meet Wilbur, so long as it is not at the pool. Addison comes in with the newspaper. Ed's photograph did not win, so there was no ridicule for him after all. Addison wants to try again the following year, but this time Wilbur says no.