This article argues that what Grice termed ‘particularized conversational implicatures’ can be divided into two types. In some cases, it is possible to reconstruct the inference from the explicit content of the utterance to the implicature without employing a premise to the effect that that the speaker expressed that content (by means of an utterance). I call these ‘material implicatures’. Those whose reconstruction relies on a premise about the speaker's verbal behaviour, by contrast, I call ‘behavioural implicatures’. After showing that the division is theoretically significant, I ask whether current pragmatic theory is able to accommodate it. I conclude that, while (neo)-Gricean pragmatics cannot do so straightforwardly, the distinction is already implicit in Relevance Theory. The article ends by considering the question of whether, in the light of previous discussion, speaker meaning really is always an instance of non-natural meaning.