Due to the foveal organization of our visual system we have to constantly move our eyes to gain precise information about our environment. Doing so massively alters the retinal input. This is problematic for the perception of moving objects, because physical motion and retinal motion become decoupled and the brain has to discount the eye movements to recover the speed of moving objects. Two different types of eye movements, pursuit and saccades, are combined for tracking. We investigated how the way we track moving targets can affect the perceived target speed. We found that the execution of corrective saccades during pursuit initiation modifies how fast the target is perceived compared with pure pursuit. When participants executed a forward (catch-up) saccade they perceived the target to be moving faster. When they executed a backward saccade they perceived the target to be moving more slowly. Variations in pursuit velocity without corrective saccades did not affect perceptual judgments. We present a model for these effects, assuming that the eye velocity signal for small corrective saccades gets integrated with the retinal velocity signal during pursuit. In our model, the execution of corrective saccades modulates the integration of these two signals by giving less weight to the retinal information around the time of corrective saccades.