A psychiatrist tells stories of four special cases to a colleague.

In a late-night meeting at his modern asylum, Dr. Tremayne (Donald Pleasence) receives visiting colleague Nicholas (Jack Hawkins) and recounts the histories of four unusual patients whose cases he has solved. In "Mr. Tiger", Paul (Russell Lewis), the sensitive young son of wealthy but constantly bickering parents, befriends an imaginary tiger. In "Penny Farthing", antiques dealer Timothy (Peter McEnery) inherits a penny-farthing bicycle which seems to have time-travel capabilities, as overseen by the apparently haunted portrait of Uncle Albert (Frank Forsyth). In "Mel", Brian (Michael Jayston) prominently displays a human-shaped dead tree in his home as a piece of found art, angering his jealous wife Bella (Dame Joan Collins). In "Luau", flamboyant literary agent Auriol (Kim Novak) hosts new client Kimo (Michael Petrovitch). Despite Auriol's overtures, he seems more interested in Auriol's beautiful daughter Ginny (Mary Tamm). As Ginny leaves for a mysterious holiday, Kimo's assistant helps Auriol prepare an elaborate luau for Kimo.