Computational modeling is a cornerstone of cognitive science. As such, computational feasibility is an important element of any linguistic theory with claims to cognitive plausibility. This article considers the computational feasibility of the conceptual integration theory of Fauconnier and Turner, and by tying together established work on the computational properties of semantic networks, analogical reasoning and metaphor comprehension, concludes that conceptual integration is indeed a computationally sound theory. One particular computational model, named Sapper, is described in detail, and the information-processing requirements of this model are used to argue for some computationally motivated extensions to the established perspective on integration.