The responses of auditory neurons tuned to stimulus intensity (i.e., nonmonotonic rate-level responders) have typically been analyzed with stimulus paradigms that eliminate neuronal adaptation to recent stimulus statistics. This procedure is usually accomplished by presenting individual sounds with long silent periods between them. Studies using such paradigms have led to hypotheses that nonmonotonic neurons may play a role in amplitude spectrum coding or level-invariant representations of complex spectral shapes. We have previously proposed an alternate hypothesis that level-tuned neurons may represent specialized coders of low sound levels because they preserve their sensitivity to low levels even when average sound level is relatively high. Here we demonstrate that nonmonotonic neurons in awake marmoset primary auditory cortex accomplish this feat by adapting their upper dynamic range to encode sounds with high mean level, leaving the lower dynamic range available for encoding relatively rare low-level sounds. This adaptive behavior manifests in nonmonotonic relative to monotonic neurons as 1) a lesser amount of overall shifting of rate-level response thresholds and (2) a nonmonotonic gain adjustment with increasing mean stimulus level.