It is not known whether psychophysical performance depends primarily on small numbers of neurons optimally tuned to specific visual stimuli, or on larger populations of neurons that vary widely in their properties. Tuning bandwidths of single cells can provide important insight into this issue, yet most bandwidth measurements have been made using suprathreshold visual stimuli, whereas psychophysical measurements are frequently obtained near threshold. We therefore examined the directional tuning of cells in the middle temporal area (MT, or V5) using perithreshold, stochastic motion stimuli that we have employed extensively in combined psychophysical and physiological studies. The strength of the motion signal (coherence) in these displays can be varied independently of its direction. For each MT neuron, we characterized the directional bandwidth by fitting Gaussian functions to directional tuning data obtained at each of several motion coherences. Directional bandwidth increased modestly as the coherence of the stimulus was reduced. We then assessed the ability of MT neurons to discriminate opposed directions of motion along six equally spaced axes of motion spanning 180 degrees. A signal detection analysis yielded neurometric functions for each axis of motion, from which neural thresholds could be extracted. Neural thresholds remained surprisingly low as the axis of motion diverged from the neuron's preferred-null axis, forming a plateau of high to medium sensitivity that extended approximately 45 degrees on either side of the preferred-null axis. We conclude that directional tuning remains broad in MT when motion signals are reduced to near-threshold values. Thus directional information is widely distributed in MT, even near the limits of psychophysical performance. These observations support models in which relatively large numbers of signals are pooled to inform psychophysical decisions.