There has been a recent spate of work on recursion as a central design feature of language and specifically of syntax. This short report points out that there is little evidence that unlimited recursion, understood as centre embedding, is typical of natural language syntax. Nevertheless, embedded pragmatic construals seem available in every language. Further, much deeper centre embedding can be found in dialogue or conversation structure than can be found in syntax. Existing accounts for the ‘performance’ limitations on centre embedding are thus thrown in doubt. Dialogue materials suggest that centre embedding is perhaps a core part of the human interaction system and is for some reason much more highly restricted in syntax than in other aspects of cognition