An emergent approach to story generation by computer is characterized by a lack of predetermined plot and a focus on character interaction forming the material for stories. A potential problem is that no interesting story emerges. However, improvisational theater shows that - at least for human actors - a predetermined plot is not necessary for creating a compelling story. There are some principles that make a successful piece of improvisational theater more than a random interaction, and these principles may inform the type of computational processes that an emergent narrative architecture draws from. We therefore discuss some of these principles, and show how these are explicitly or implicitly used in story generation and interactive storytelling research. Finally we draw lessons from these principles and ask attention for two techniques that have been little investigated: believably incorporating directives, and late commitment.