Intensity variation poses a fundamental problem for sensory discrimination because changes in the response of sensory neurons as a result of stimulus identity, e.g., a change in the identity of the speaker uttering a word, can potentially be confused with changes resulting from stimulus intensity, for example, the loudness of the utterance. Here we report on the responses of neurons in field L, the primary auditory cortex homolog in songbirds, which allow for accurate discrimination of birdsongs that is invariant to intensity changes over a large range. Such neurons comprise a subset of a population that is highly diverse, in terms of both discrimination accuracy and intensity sensitivity. We find that the neurons with a high degree of invariance also display a high discrimination performance, and that the degree of invariance is significantly correlated with the reproducibility of spike timing on a short time scale and the temporal sparseness of spiking activity. Our results indicate that a temporally sparse spike timing-based code at a primary cortical stage can provide a substrate for intensity-invariant discrimination of natural sounds.