Smooth pursuit of natural objects requires flexible allocation of attention to inspect features. However, it has been reported that attention is focused at the fovea during pursuit. We ask here if foveal attention is obligatory during pursuit, or if it can be disengaged. Observers tracked a stimulus composed of a central dot surrounded by four others and identified one of the dots when it dimmed. Extinguishing the center dot before the dimming improved task performance, suggesting that attention was released from it. To determine if the center dot automatically usurped attention, we provided the pursuit system with an alternative sensory signal by adding peripheral motion that moved with the stimulus. This also improved identification performance, evidence that a central target does not necessarily require attention during pursuit. Identification performance at the central dot also improved, suggesting that the spatial extent of the background did not attract attention to the periphery; instead, peripheral motion freed pursuit attention from the central dot, affording better identification performance. The results show that attention can be flexibly allocated during pursuit and imply that attention resources for pursuit of small and large objects come from different sources.