How does the knowledge shared by interlocutors during interaction modify the way speakers speak? Specifically, how does prosody change when speakers know that their addressees do not share the same knowledge as them? We studied these effects in an interactive paradigm in which French speakers gave instructions to addressees about where to place a cross between different objects (e.g., You put the cross between the red mouse and the red house). We manipulated (i) whether the two interlocutors shared or did not necessarily share the same objects and (ii) the informational status of referents. We were interested in two types of prosodic variations: global prosodic variations that affect entire utterances (i.e., pitch range and speech rate variations) and more local prosodic variations that encode informational status of referents (i.e., prosodic phrasing for French). We found that participants spoke more slowly and with larger pitch excursions in the not-shared knowledge condition than in the shared knowledge condition while they did not prosodically encode the informational status of referents regardless of the knowledge condition. Results demonstrated that speakers kept track of what the addressee knew, and that they adapted their global prosody to their interlocutors. This made the task too cognitively demanding to allow the prosodic encoding of the informational status of referents. Our findings are in line with the idea that complex reasoning usually implicated in constructing a model of the addressee co-exists with speaker-internal constraints such as cognitive load to affect speaker's prosody during interaction.