Behavioral states marked by varying levels of arousal and attention modulate some properties of cortical responses (e.g. average firing rates or pairwise correlations), yet it is not fully understood what drives these response changes and how they might affect downstream stimulus decoding. Here we show that changes in state modulate the tuning of response variance-to-mean ratios (Fano factors) in a fashion that is neither predicted by a Poisson spiking model nor changes in the mean firing rate, with a substantial effect on stimulus discriminability. We recorded motion-sensitive neurons in middle temporal cortex (MT) in two states: alert fixation and light, opioid anesthesia. Anesthesia tended to lower average spike counts, without decreasing trial-to-trial variability compared to the alert state. Under anesthesia, within-trial fluctuations in excitability were correlated over longer time scales compared to the alert state, creating supra-Poisson Fano factors. In contrast, alert-state MT neurons have higher mean firing rates and largely sub-Poisson variability that is stimulus-dependent and cannot be explained by firing rate differences alone. The absence of such stimulus-induced variability tuning in the anesthetized state suggests different sources of variability between states. A simple model explains state-dependent shifts in the distribution of observed Fano factors via a suppression in the variance of gain fluctuations in the alert state. A population model with stimulus-induced variability tuning and behaviorally constrained information-limiting correlations explores the potential enhancement in stimulus discriminability by the cortical population in the alert state.