Interlocutors tend to refer to objects using the same names as each other. We investigated whether native and non-native interlocutors’ tendency to do so is influenced by speakers’ nativeness and by their beliefs about an interlocutor's nativeness. A native or non-native participant and a native or non-native confederate directed each other around a map to deliver objects to locations. We manipulated whether confederates referred to objects using a favored or disfavored name, while controlling for confederates’ language behavior. We found evidence of audience design for native and non-native addressees: participants were more likely to use a disfavored name after a non-native confederate used that name than after a native confederate used that name; this tendency did not differ between native and non-native participants. Results suggest that both native and non-native speakers can adapt to the language of non-native partners through non-automatic, goal-directed mechanisms of alignment during cognitively demanding communicative tasks.