This paper deals with a theory-internal problem inherent in current pragmatic theories which Levinson (2000) dubbed ‘Grice’s circle’. The expression ‘circle’ stems from the fact that conversational implicatures take their input from truth-conditional content, whereas the latter is constituted on the basis of pragmatic augmentations. The paper deals with a conversational fragment whose analysis can contribute to the understanding of the semantics/pragmatics debate (by providing a clear-cut and irreducible example of pragmatic intrusion) and of Grice’s circle. After ample discussion of the current literature, the paper explores a logical possibility: explicatures (or implicitures) are non-cancellable: hence there is a way out of the apparently vicious circularity called ‘Grice’s circle’. It follows that conversational implicatures take their input from contextually supplied, non-cancellable truth-conditional content and that a neat distinction can still be made between meaning augmentations that are cancellable (conversational implicatures) and those that are not.