Speakers often do not state requests directly but employ innuendos such as "Would you like to see my etchings?" Though such indirectness seems puzzlingly inefficient, it can be explained by a theory of the "strategic speaker", who seeks plausible deniability when he or she is uncertain of whether the hearer is cooperative or antagonistic. A paradigm case is bribing a policeman who may be corrupt or honest: A veiled bribe may be accepted by the former and ignored by the latter. Everyday social interactions can have a similar payoff structure (with emotional rather than legal penalties) whenever a request is implicitly forbidden by the relational model holding between speaker and hearer (e.g., bribing an honest maitre d', where the reciprocity of the bribe clashes with his authority). Even when a hearer's willingness is known, indirect speech offers higher-order plausible deniability by preempting certainty, gossip, and common knowledge of the request. In supporting experiments, participants judged the intentions and reactions of characters in scenarios that involved fraught requests varying in politeness and directness. (Contains 8 figures, 6 tables and 8 footnotes.)