Eavesdropping on interactions between conspecific animals provides a low-cost method for assessing other individuals. Asymmetries in territorial counter-singing interactions in songbirds provide a rich source of information for eavesdroppers about differences between the singers. Yet, little is known about the relationship between interactive singing in a natural, low-arousal context among territorial neighbours and individual traits of males. We used a microphone array to monitor natural counter-singing interactions in great tits (Parus major) during nest building, at the onset of the breeding season. We quantified song overlapping and song matching for 30 pairs (dyads) of interacting males, singing at their nest, respectively. We then compared these behaviours to five traits for 28 males: body condition, plumage ornamentation, offspring provisioning behaviour, offspring weight and breeding site quality. We found no relationship between a male song overlapping or matching behaviour and any of the measured traits. Therefore, our results do not support the idea that short-term asymmetries in low-arousal long-range singing interactions among neighbours reflect differences in these fitness-related traits. Instead, our findings suggest that such singing asymmetries have less signal value in the absence of an immediate conflict but instead reflect short-term motivational differences, as shown in previous investigations.