In this paper we present a critique of pure insertion. Pure insertion represents an implicit assumption behind many (but not all) studies that employ cognitive subtraction. The main contention is that pure insertion is not valid in relation to the neuronal instantiation of cognitive processes. Pure insertion asserts that there are no interactions among the cognitive components of a task. It is possible to evaluate and refute this assumption by testing explicitly for interactions using factorial experimental designs. It is proposed that factorial designs are more powerful than subtraction designs in characterizing cognitive neuroanatomy, precisely because they allow for interactions and eschew notions like pure insertion. In particular we suggest that the effect of a cognitive component (i.e., an effect that is independent of other components) is best captured by the main (activation) effect of that component and that the integration among components (i.e., the expression of one cognitive process in the context of another) can be assessed with the interaction terms. In this framework a complete characterization of cognitive neuroanatomy includes both regionally specific activations and regionally specific interactions. To illustrate our point we have used a factorial experimental design to show that inferotemporal activations, due to object recognition, are profoundly modulated by phonological retrieval of the object's name. This interaction implicates the inferotemporal regions in phonological retrieval, during object naming, despite the fact that phonological retrieval does not, by itself, activate this region.