In this paper I take up the idea that human thinking is systematically biased in the direction of interactive thinking (E. Goody's anticipatory interactive planning), that is, that humans are peculiarly good at, and inordinately prone to, attributing intentions and goals to one other (as well as to non-humans), and that they routinely orient to presumptions about each other's intentions in what they say and do. I explore the implications of that idea for an understanding of politeness in interaction, taking as a starting point the Brown and Levinson (1987) model of politeness, which assumes interactive thinking, a notion implicit in the formulation of politeness as strategic orientation to face. Drawing on an analysis of the phenomenon of conventionalized ‘irony’ in Tzeltal, I emphasize that politeness does not inhere in linguistic form per se but is a matter of conveying a polite intention, and argue that Tzeltal irony provides a prime example of one way in which humans' highly-developed intellectual machinery for inferring alter's intentions is put to the service of social relationships.