A shuttle pilot on the outer fringes of space finds a stowaway on board his ship. Because of the extra weight, he does not have enough fuel for his journey and faces a dilemma forcing him to consider jettisoning her into space.

A Mrs Ernestine Todd, from Clapham, asks Poirot to help her find her cook, Eliza, who has disappeared. Poirot, who aims to accept only really significant cases, is at first insulted by such a trivial request. However, after he sees the contents of the missing cook's trunk, he decides the case could prove to be worthy of his talents.