We assessed the ability to extract velocity information from brief exposure of a moving target and sought evidence that this information could be used to modulate the extra-retinal component of ocular pursuit. A step-ramp target motion was initially visible for a brief randomised period of 50, 100, 150 or 200ms, but then extinguished for a randomised period of 400 or 600ms before reappearing and continuing along its trajectory. Target speed (5-20deg/s), direction (left/right) and inter-trial interval (2.7-3.7s) were also randomised. Smooth eye movements were initiated after ~130ms and comprised an initial visually-dependent component, which reached a peak velocity that increased with target velocity and initial exposure duration, followed by a sustained secondary component that actually increased throughout extinction for 50 and 100ms initial exposures. End-extinction eye velocity, reflecting extra-retinal drive, increased with initial exposure from 50-100ms but remained similar for longer exposures; it was significantly scaled to target velocity for 150 and 200ms exposures. The results suggest that extra-retinal drive is based on a sample of target velocity, mostly acquired during the first 150ms, that is stored and forms a goal for generating appropriately scaled eye movements during absence of visual input. End-extinction eye velocity was significantly higher when target reappearance was expected than when it was not, confirming the importance of expectation in generating sustained smooth movement. However, end-extinction eye displacement remained similar irrespective of expectation, suggesting that the ability to use sampled velocity information to predict future target displacement operates independently of the control of smooth eye movement.