[5] The first story in the collection tells of a group of yellow bird-like creatures called the Sneetches, some of whom have a green star on their bellies.

An entrepreneur/con-artist named Sylvester McMonkey McBean (calling himself the Fix-It-Up Chappie) appears and offers the Sneetches without stars the chance to get them with his Star-On machine, for three dollars.

McBean then tells them about his Star-Off machine, costing ten dollars, and the Sneetches who originally had stars happily pay the money to have them removed in order to remain special.

Because they stubbornly refuse to move (east, west, or any direction except their respective headings) to get past each other, the two Zax then face off against each other with their arms crossed.

This causes minor problems in the family when she calls one of them, but instead, they all come, and the rest of the story lists unusual and amusing names she wishes she had given them, such as "Bodkin Van Horn", "Hoos Foos", "Snimm", "Hot-Shot", "Shadrack", "Stuffy", "Stinky", "Putt-Putt", "Buffalo Bill", "Oliver Boliver Butt", "Biffalo Buff" or "Zanzibar Buck-Buck McFate".

In 1998, NATO translated the collection into Serbo-Croatian and planned to distribute 500,000 copies to children in Bosnia and Herzegovina, as part of a campaign to encourage tolerance.