This paper presents a methodology to study the role of nonnative accents on talker recognition by humans. The methodology combines a state-of-the-art accent-conversion system to resynthesize the voice of a speaker with a different accent of her/his own, and a protocol for perceptual listening tests to measure the relative contribution of accent and voice quality on speaker similarity. Using a corpus of non-native and native speakers, we generated accent conversions in two different directions: non-native speakers with native accents, and native speakers with non-native accents. Then, we asked listeners to rate the similarity between 50 pairs of real or synthesized speakers. Using a linear mixed effects model, we find that (for our corpus) the effect of voice quality is five times as large as that of non-native accent, and that the effect goes away when speakers share the same (native) accent. We discuss the potential significance of this work in earwitness identification and sociophonetics.