We have examined the characteristics of vergence-induced reduction of ocular counter-roll in near vision. Monkeys were trained to make convergent and divergent refixations with the head and body either upright or in various roll orientations. During near viewing requiring 17° horizontal vergence, we found that static binocular torsion was suppressed by about 68% (averaged over both eyes, two monkeys and both near target locations). This result is in accordance with a previous study in which binocular torsion was quantified based on the displacement planes of eye positions in far and near viewing. Latency and duration of the change in torsional eye position depended (for each eye differently) on body roll and the depth plane of fixation. For instance, during convergent refixations in left-ear-down orientations, the latencies of the left eye were smaller and the durations were longer than those of the right eye. However, both eyes reached their final positions required to fixate the second visual target at roughly the same time. The different dynamics of the two eyes is explained by the fact that each eye rotated temporally when the eyes converged, a pattern named binocular extension of Listing's law. Coming from or aiming at a common torsional value (normal ocular counter-roll) in convergent or divergent refixations, the required torsion differs in the two eyes. The brain compensates for these differences by adjusting the dynamics of each eye's movement.