To redirect our gaze in three-dimensional space we frequently combine saccades and vergence. These eye movements, known as disconjugate saccades, are characterized by eyes rotating by different amounts, with markedly different dynamics, and occur whenever gaze is shifted between near and far objects. How the brain ensures the precise control of binocular positioning remains controversial. It has been proposed that the traditionally assumed "conjugate" saccadic premotor pathway does not encode conjugate commands but rather encodes monocular commands for the right or left eye during saccades. Here, we directly test this proposal by recording from the premotor neurons of the horizontal saccade generator during a dissociation task that required a vergence but no horizontal conjugate saccadic command. Specifically, saccadic burst neurons (SBNs) in the paramedian pontine reticular formation were recorded while rhesus monkeys made vertical saccades made between near and far targets. During this task, we first show that peak vergence velocities were enhanced to saccade-like speeds (e.g., > 150deg/sec versus < 100deg/sec during saccade-free movements for comparable changes in vergence angle). We then quantified the discharge dynamics of SBNs during these movements and found that the majority of the neurons preferentially encode the velocity of the ipsilateral eye. Notably, a given neuron typically encoded the movement of the same eye during horizontal saccades that were made in depth. Taken together our findings demonstrate that the brainstem saccadic burst generator encodes integrated conjugate and vergence commands, and thus provide strong evidence for the proposal that the classic saccadic premotor pathway controls gaze in three dimensional space.