This article deals with a ticklish theoretical problem regarding the workings of conversational humour, which is often considered as a special mode/frame of communication but, concurrently, as a vehicle for communicating meanings outside this frame. The first aim is to tease out the different terms prevailing in humour research that try to capture this distinction (like playfulness, jocularity, or non-seriousness). Second, a suggestion is made in favour of the notion of (un)truthfulness, approached from a neo-Gricean viewpoint, as a concept that can help clarify this twofold problem better, giving a full spectrum of humour manifestations without generating any terminological inconsistencies. Grice's first maxim of Quality is thus cited to explain the main categories of humour discerned here: autotelic humour (which resides in opting out of this maxim) and speaker-meaning-telic humour (which communicates truthful or covertly untruthful speaker meaning by means of fulfilment, flouting or violation of this maxim and the other ones as well). Speaker meaning may arise as what is said (as a result of maxim fulfilment) and/or implicature (as a consequence of maxim flouting), and both levels of meaning may recruit maxim violations, which lead to deception. This paper adds to the discussion on the position of humour in the Gricean framework.