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Oculomotor behavior is a powerful tool to probe brain function and disease. Previous studies have shown how fixational drift velocities depend on eccentricity (Bertolini et al., 2013; Romano et al., 2017) and how fixational drift can adapt after prolonged eccentric fixation (Otero-Millan et al., 2019). Here, eighteen subjects completed two experiments where we measured drift velocity while fixating a briefly flashed target, to remove retinal slip cues. In the first experiment, we measured their baseline relationship between fixational drift velocity and eye position. In the second experiment, we investigated the adaptation of that relationship after prolonged fixation at a very eccentric position. This adaptation usually manifests by the presence of rebound nystagmus (RN) upon returning to central gaze. Our results replicate the finding that drift increases at central fixation in the direction consistent with rebound nystagmus, that is, towards the previously held eccentric position, highlighting that drift velocity depends on the history of eye positions. When examining the entire relationship between drift velocity and eye position we find a mostly linear relationship but with increased slope relative to the baseline condition. However, the adaptation of the integrator cannot be modeled by a simple change in leakiness, as that would not result in increased drift at central gaze. Other mechanisms of adaptation such as shifts in the position or velocity set-points for gaze holding could be present but are indistinguishable with the current data.