A central finding in many cortical areas is that single neurons can match behavioral performance in the discrimination of sensory stimuli. However, whether this is true for natural behaviors involving complex natural stimuli remains unknown. Here we use the model system of songbirds to address this problem. Specifically, we investigate whether neurons in field L, the homolog of primary auditory cortex, can match behavioral performance in the discrimination of conspecific songs. We use a classification framework based on the (dis)similarity between single spike trains to quantify neural discrimination. We use this framework to investigate the discriminability of single spike trains in field L in response to conspecific songs, testing different candidate neural codes underlying discrimination. We find that performance based on spike timing is significantly higher than performance based on spike rate and interspike intervals. We then assess the impact of temporal correlations in spike trains on discrimination. In contrast to widely discussed effects of correlations in limiting the accuracy of a population code, temporal correlations appear to improve the performance of single neurons in the majority of cases. Finally, we compare neural performance with behavioral performance. We find a diverse range of performance levels in field L, with neural performance matching behavioral accuracy only for the best neurons using a spike-timing-based code.