While the tendency of speakers to align their speech to that of others acoustic-phonetically has been widely studied among native speakers, very few studies have examined whether natives phonetically converge to non-native speakers. Here we measured native Dutch speakers’ convergence to a non-native speaker with an unfamiliar accent in a novel non-interactive task. Furthermore, we assessed the role of participants’ perceptions of the non-native accent in their tendency to converge. In addition to a perceptual measure (AXB ratings), we examined convergence on different acoustic dimensions (e.g., vowel spectra, fricative CoG, speech rate, overall f0) to determine what dimensions, if any, speakers converge to. We further combined these two types of measures to discover what dimensions weighed in raters’ judgments of convergence. The results reveal overall convergence to our non-native speaker, as indexed by both perceptual and acoustic measures. However, the ratings suggest the stronger participants rated the non-native accent to be, the less likely they were to converge. Our findings add to the growing body of evidence that natives can phonetically converge to non-native speech, even without any apparent socio-communicative motivation to do so. We argue that our results are hard to integrate with a purely social view of convergence.