The minimal change in a stimulus property that is detectable by neurons has been often quantified using the receiver operating characteristic (ROC) curve, but recent studies introduced the use of the related Fisher information (FI). Whereas ROC analysis and FI quantify the information available for discriminating between two stimuli, global aspects of the information carried by a neuron are quantified by the mutual information (MI) between stimuli and responses. FI and MI have been shown to be related to each other when FI is large. Here the responses of neurons recorded in the inferior colliculus of anesthetized guinea pigs in response to ensembles of sounds differing in their interaural time differences (ITDs) or binaural correlation (BC) were analyzed. Although the FI is not uniformly large, there are strong relationships between MI and FI. Information-theoretic measures are used to demonstrate the importance of the non-Poisson statistics of these responses. These neurons may reflect the maximization of the MI between stimuli and responses under constraints on the coded stimulus range and the range of firing rates. Remarkably, whereas the maximization of MI, in conjunction with the non-Poisson statistics of the spike trains, is enough to create neurons whose ITD discrimination capabilities are close to the behavioral limits, the same rule does not achieve single-neuron BC discrimination that is as close to behavioral performance.