Sometimes it is thought that there are serious differences between theories of discourse that turn on the role of cognition in the theory. This is largely a misconception: for example, with its emphasis on participants’ own understandings, its principles of recipient design and projection, Conversation Analysis is hardly anti-cognitive. If there are genuine disagreements they rather concern a preference for ‘lean’ versus ‘rich’ metalanguages and different methodologies. The possession of a multi-levelled model, separating out what the individual brings to interaction from the emergent properties of interaction, would make it easier to resolve some of these issues. Meanwhile, these squabbles on the margins distract us from a much more central and more interesting issue: is there a very special cognition-for-interaction, which underlies and underpins all language and discourse? Prime facie evidence suggests that there is, and different approaches can contribute to our understanding of it.