Human intentional communication is marked by its flexibility and context sensitivity. Hypothesized brain mechanisms can provide convincing and complete explanations of the human capacity for intentional communication only insofar as they can match the computational power required for displaying that capacity. It is thus of importance for cognitive neuroscience to know how computationally complex intentional communication actually is. Though the subject of considerable debate, the computational complexity of communication remains so far unknown. In this paper we defend the position that the computational complexity of communication is not a constant, as some views of communication seem to hold, but rather a function of situational factors. We present a methodology for studying and characterizing the computational complexity of communication under different situational constraints. We illustrate our methodology for a model of the problems solved by receivers and senders during a communicative exchange. This approach opens the way to a principled identification of putative model parameters that control cognitive processes supporting intentional communication.