Single sensory neurons can be surprisingly predictive of behavior in discrimination tasks. We propose this is possible because sensory information extracted from neural populations is severely restricted, either by near-optimal decoding of a population with information-limiting correlations or by suboptimal decoding that is blind to correlations. These have different consequences for choice correlations, the correlations between neural responses and behavioral choices. In the vestibular and cerebellar nuclei and the dorsal medial superior temporal area, we found that choice correlations during heading discrimination are consistent with near-optimal decoding of neuronal responses corrupted by information-limiting correlations. In the ventral intraparietal area, the choice correlations are also consistent with the presence of information-limiting correlations, but this area does not appear to influence behavior, although the choice correlations are particularly large. These findings demonstrate how choice correlations can be used to assess the efficiency of the downstream readout and detect the presence of information-limiting correlations.