This paper proposes a new analysis of indirect speech in the framework of game theory, social psychology, and evolutionary psychology. It builds on the theory of Grice, which tries to ground indirect speech in pure rationality (the demands of e‰cient communication between two cooperating agents) and on the Politeness Theory of Brown and Levinson, who proposed that people cooperate not just in exchanging data but in saving face (both the speaker’s and the hearer’s). I suggest that these theories need to be supple- mented because they assume that people in conversation always cooperate. A reflection on how a pair of talkers may have goals that conflict as well as coincide requires an examination of the game-theoretic logic of plausible denial, both in legal contexts, where people’s words may be held against them, and in everyday life, where the sanctions are social rather than judi- cial. This in turn requires a theory of the distinct kinds of relationships that make up human social life, a consideration of a new role for common knowledge in the use of indirect speech, and ultimately the paradox of ra- tional ignorance, where we choose not to know something relevant to our interests.