Recent Iterated Response (IR) models of pragmatics conceptualize language use as a recursive process in which agents reason about each other to increase communicative efficiency. These models are generally defined over complete utterances. However, there is substantial evidence that pragmatic reasoning takes place incrementally during production and comprehension. We address this with an incremental IR model. We compare the incremental and global versions using computational simulations, and we assess the incremental model against existing experimental data and in the TUNA corpus for referring expression generation, showing that the model can capture phenomena out of reach of global versions.