Cerebellar output changes during motor learning. How these changes cause alterations of motoneuron activity and movement remains an unresolved question for voluntary movements. To answer this question, we examined premotor neurons for saccadic eye movement. Previous studies indicate that cells in the fastigial oculomotor region (FOR) within the cerebellar nuclei on one side exhibit a gradual increase in their saccade-related discharge as the amplitude of ipsiversive saccades adaptively decreases. This change in FOR activity could cause the adaptive change in saccade amplitude because neurons in the FOR project directly to the brainstem region containing premotor burst neurons (BNs). To test this possibility, we recorded the activity of saccade-related burst neurons in the area that houses premotor inhibitory burst neurons (IBNs) and examined their discharge during amplitude-reducing adaptation elicited by intrasaccadic target steps. We specifically analyzed their activity for off-direction (contraversive) saccades, in which the IBN activity would increase to reduce saccade size. Before adaptation, 29 of 42 BNs examined discharged, at least occasionally, for contraversive saccades. As the amplitude of contraversive saccades decreased adaptively, half of BNs with off-direction spike activity showed an increase in the number of spikes (14/29) or an earlier occurrence of spikes (7/14). BNs that were silent during off-direction saccades before adaptation remained silent after adaptation. These results indicate that the changes in the off-direction activity of BNs are closely related to adaptive changes in saccade size and are appropriate to cause these changes.