When people speak, they often insinuate their intent indirectly rather than stating it as a bald proposition. Examples include sexual come-ons, veiled threats, polite requests, and concealed bribes. We propose a three-part theory of indirect speech, based on the idea that human communication involves a mixture of cooperation and conflict. First, indirect requests allow for plausible deniability, in which a cooperative listener can accept the request, but an uncooperative one cannot react adversarially to it. This intuition is sup- ported by a game-theoretic model that predicts the costs and benefits to a speaker of direct and indirect requests. Second, language has two functions: to convey information and to negotiate the type of relationship holding between speaker and hearer (in particu- lar, dominance, communality, or reciprocity). The emotional costs of a mismatch in the assumed relationship type can create a need for plausible deniability and, thereby, select for indirectness even when there are no tangible costs. Third, people perceive language as a digital medium, which allows a sentence to generate common knowledge, to propagate a message with high fidelity, and to serve as a reference point in coordination games. This feature makes an indirect request qualitatively different from a direct one even when the speaker and listener can infer each other’s intentions with high confidence.