Most uses of mais (‘but’) as a connector in French (i.e. correction, opposition, concession) imply a contrast between their antecedent p and their scope q but differ in terms of argumentative orientation. Conversely, p and q in overbid mais (‘des grands mecs mais très grands!’ 'tall guys mais very tall!') present a co-oriented argumentation and the contrast is expressed by a semantic strengthening from p to q. We hypothesized that this should be reflected by both a lexical and a prosodic strengthening of the scope constituent q. To test this hypothesis, we compared the overbid use with the concessive use in conversational data. We found more adverbial intensifiers in the scope of the overbid than the concessive use. We also investigated both the phonetic and phonological realisation of mais itself and of its scope. We found that both mais are phrased with their scope rather than alone. Crucially, we found a significantly greater H tone rate (both per second and per syllable) on the scope of the overbid. We also found a lower articulation rate but only in the absence of adverbial intensifiers. This demonstrates the role of tonal density in prosodic strengthening.