Primates are capable of discriminating depth with remarkable precision using binocular disparity. Neurons in area V4 are selective for relative disparity, which is the crucial visual cue for discrimination of fine disparity. Here, we investigated the contribution of V4 neurons to fine disparity discrimination. Monkeys discriminated whether the center disk of a dynamic random-dot stereogram was in front of or behind its surrounding annulus. We first behaviorally tested the reference frame of the disparity representation used for performing this task. After learning the task with a set of surround disparities, the monkey generalized its responses to untrained surround disparities, indicating that the perceptual decisions were generated from a disparity representation in a relative frame of reference. We then recorded single-unit responses from V4 while the monkeys performed the task. On average, neuronal thresholds were higher than the behavioral thresholds. The most sensitive neurons reached thresholds as low as the psychophysical thresholds. For subthreshold disparities, the monkeys made frequent errors. The variable decisions were predictable from the fluctuation in the neuronal responses. The predictions were based on a decision model in which each V4 neuron transmits the evidence for the disparity it prefers. We finally altered the disparity representation artificially by means of microstimulation to V4. The decisions were systematically biased when microstimulation boosted the V4 responses. The bias was toward the direction predicted from the decision model. We suggest that disparity signals carried by V4 neurons underlie precise discrimination of fine stereoscopic depth.