The offer of some cake can be declined by saying “I am on a diet” – an indirect reply. Here, we asked whether certain well-established psychological and conceptual features are linked to the (in)directness of speech acts – an issue unexplored so far. Subjects rated direct and indirect speech acts performed by the same critical linguistic forms in different dialogic contexts. We find that indirect replies were understood with less certainty, were less predictable by, less coherent with and less semantically similar to their context question. These effects were smaller when direct and indirect replies were matched for the type of speech acts for which they were used, compared to when they were not speech act matched. Crucially, all measured cognitive dimensions were strongly associated with each other. These findings suggest that indirectness goes hand-in-hand with a set of cognitive features, which should be taken into account when interpreting experimental findings, including neuroimaging studies of indirectness.