In this paper, I propose that the exhaustive interpretation associated with Hungarian Focus Fronting (FF) is a conventional implicature that belongs to the non-at-issue dimension of meaning and that is directly responsible for the syntactic displacement of the focus constituent. Following a cartographic approach, I defend the view that the interface properties that result from FF, including the associated implicatures at the semantic level, are directly encoded in the syntax in the form of active syntactic features which drive the movement of sentential constituents to dedicated functional projections. In the case of FF, more specifically, these features trigger syntactic movement and generate the relevant implicature. This proposal is based on the observation that, despite being a prominent one – and perhaps the most prominent – the exhaustive reading is not the only possible interpretation that can be associated with FF in Hungarian. Other meanings can be associated with FF in the relevant contexts and under the appropriate conditions, for example, a mirative import of surprise and unexpectedness that need not be exhaustive. From a crosslinguistic viewpoint, moreover, this account provides an explanation for the fact that the exhaustive reading associated with FF, especially in answers to questions, appear to be a language specific property of Hungarian.