Great storytellers know how to take us on a journey. They direct characters to act -- not necessarily in the most rational way -- but rather in a way that leads to interesting situations, and ultimately creates an impactful experience for audience members looking on. If audience experience is what matters most, then can we help artists and animators *directly* craft such experiences, independent of the concrete character actions needed to evoke those experiences? In this paper, we offer a novel computational framework for such tools. Our key idea is to optimize animations with respect to *simulated* audience members' experiences. To simulate the audience, we borrow an established principle from cognitive science: that human social intuition can be modeled as "inverse planning," the task of inferring an agent's (hidden) goals from its (observed) actions. Building on this model, we treat storytelling as "*inverse* inverse planning," the task of choosing actions to manipulate an inverse planner's inferences. Our framework is grounded in literary theory, naturally capturing many storytelling elements from first principles. We give a series of examples to demonstrate this, with supporting evidence from human subject studies.