Directed improvisation is a new paradigm for multiagent interaction. One or more human users direct one or more computer characters with scripted or interactive directions. The characters work together to improvise a course of behavior that follows the directions, expresses their distinctive individual styles, honors social conventions, and meets other objectives. The resulting "performance" reflects the collaboration among all of the human and computer agents. Directed improvisation has several attractive properties as a paradigm for multiagent human-computer interaction, which we illustrate in our testbed application, an animated improvisational theater company for children. Directed improvisation also presents distinctive requirements for agent interaction (emphasizing: situated, spontaneous, opportunistic behavior; very intimate interaction with shared control; and process-oriented evaluation criteria), which make it useful addition to the domain of inquiry for multiagent systems.