Although systematic preparation is a key factor in negotiation success, negotiators often become ensnared in their own planning. Negotiators sometimes do not reveal what they really want, fail to discern hidden agendas, or dwell on arguments of little importance. This article proposes viewing negotiation as a paradox called structured spontaneity. It explains how three fundamental levels of awareness exist in every negotiation. Positions are what the other side claims it wants, often in the form of a simple demand; Interests may underlie these stated positions; and Perceptions reflect how the negotiating partner sees the world. Building on this, the authors propose an “improvisational iceberg” with three more levels. Head is where the discovery of the other side’s position takes place; Heart is where we invite connections between interests and keep open minds; and Core constitutes business philosophy and corporate culture. Structured spontaneity in negotiations can be taught through improvisation training. In switch games, actors play out improvised scenarios and swap roles; in wordless negotiation, participants try to convey what they want non-verbally; in monologues, negotiators tap into the Core of the other side. Ultimately, improvisational training for negotiators is about the tension between strategic preparation and willingness to follow the other side in a new direction on short notice.