People tell stories about not only the past, but also the future, particularly when contemplating difficult decisions. When such stories are constructed aloud, in conversation, the potential for disagreement is pervasive because no one can claim to have witnessed the future and thus no one can claim the sole right to narrate it. Consequently, storytelling procedures need to be broadened to accommodate a diversity of opinions about causes and consequences. This article argues that those procedures are based on an expanded notion of narrative relevance, and illustrates their operation in the deliberations of the Executive Committee of the National Security Council during the Cuban missile crisis. These storytelling procedures provided scaffolding for the deliberations about possible U.S. responses after the discovery of Soviet missiles; they delimited the "moving front" for skirmishes around possible scenarios and outcomes; and they were partly constitutive of the discursive grounds for Kennedy's decisions.