Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we reinforced the least frequent saccadic amplitudes to increase variability, and then reinforced the central part of the amplitude distributions to reduce variability. The target was placed at a constant distance from the fovea after the saccade to maintain the postsaccadic visual signal constant and an auditory reinforcement was delivered depending on saccadic amplitude. The second experiment tested the effects of the contingency. We reinforced high levels of variability in 4 participants, whereas 4 other participants were assigned to a yoked control group. On average, saccadic amplitude standard deviations were doubled while the medians remained mostly unchanged in the experimental participants in both experiments, and variability returned to baseline level when low variability was reinforced. In the control group no consistent changes in amplitude distributions were observed. These results, showing that variability can be reinforced, challenge the idea of a stochastic neural noise. We instead propose that selection processes constrain saccadic amplitude distributions.