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H. P. Grice first presented his theory of conversational implicature in “Logic and Conversation.” This theory is comprised of conversational maxims that are based on the Cooperative Principle. Since then, it has become the default theory of implicature in pragmatics. This theory, however, is deeply flawed. Asa Kasher and Wayne Davis present alternative models for conversational implicature, but they both also have shortcomings in their theories. This work attempts to reconcile the Gicean theory of implicature with Kasher’s rationality based theory, and Davis’ theory of implicatures as conventions. The theory presented here creates conversational kinds to distinguish between cooperative conversation and non-cooperative conversation. Conversational implicature is convention based, but the conversational maxims are retained for cooperative conversational kinds. Thus, maxim violations end up as conversational cues informing participants that irrational statements may be better understood within a conventional framework. This provides for the shortcomings of the earlier works, and has greater explanatory power.