Amplitude modulation (AM) is a common feature of natural sounds, and its detection is biologically important. Even though most sounds are not fully modulated, the majority of physiological studies have focused on fully modulated (100% modulation depth) sounds. We presented AM noise at a range of modulation depths to awake macaque monkeys while recording from neurons in primary auditory cortex (A1). The ability of neurons to detect partial AM with rate and temporal codes was assessed with signal detection methods. On average, single-cell synchrony was as or more sensitive than spike count in modulation detection. Cells are less sensitive to modulation depth if tested away from their best modulation frequency, particularly for temporal measures. Mean neural modulation detection thresholds in A1 are not as sensitive as behavioral thresholds, but with phase locking the most sensitive neurons are more sensitive, suggesting that for temporal measures the lower-envelope principle cannot account for thresholds. Three methods of preanalysis pooling of spike trains (multiunit, similar to convergence from a cortical column; within cell, similar to convergence of cells with matched response properties; across cell, similar to indiscriminate convergence of cells) all result in an increase in neural sensitivity to modulation depth for both temporal and rate codes. For the across-cell method, pooling of a few dozen cells can result in detection thresholds that approximate those of the behaving animal. With synchrony measures, indiscriminate pooling results in sensitive detection of modulation frequencies between 20 and 60 Hz, suggesting that differences in AM response phase are minor in A1.