According to Steven Pinker and his associates the cooperative model of human communication fails, because evolutionary biology teaches us that most social relationships, including talk-exchange, involve combinations of cooperation and conflict. In particular, the phenomenon of the strategic speaker who uses indirect speech in order to be able to deny what he meant by a speech act (deniability of conversational implicatures) challenges the model. In reply I point out that interlocutors can aim at understanding each other (cooperation), while being in conflict. Furthermore, Pinker’s strategic speaker relies on the Cooperative Principle when conveying a conversational implicature, and so non-cooperative behaviour (denial) only emerges as a response to a negative reaction from the audience. It is also doubtful in the cases Pinker presents whether a denial will successfully cancel the conversational implicature –change the audience’s interpretation of speaker’s meaning. I also argue that a strategic speaker might choose indirect speech due to the ignorability of conversational implicatures, in which case the strategic speaker can be highly cooperative.