We present a computational model exploring goal-directed deployment of attention during object tracking. Once selected, objects are tracked in parallel, but serial attention can be directed to an object that is visually crowded and in danger of being lost. An attended object’s future position can be extrapolated from its past motion trajectory, allowing the object to be tracked even when it is briefly occluded. Using the model, we demonstrate that the difficulty of tracking through occlusions increases with the number of objects because they compete for serial attention.