The human vision system appears to divide into two streams: a ventral stream from V1 to the inferior temporal cortex processing 'vision for perception', and a dorsal stream from V1 to the posterior parietal cortex processing 'vision for action'. Among other characteristics, it has been suggested that dorsal processing is effortless, unconscious, and not bearing on central cognitive resources implicated in ventral processing. The present study shows that a typical dorsal task (i.e., grasping an object) is subject to a classical indicator of capacity limitations in dual-task situations, the psychological refractory period (PRP) effect. In particular, response times to task 2 (the grasping task) increased the more the two tasks overlapped in time, i.e., the shorter the time interval between the stimuli of the two tasks was. As is also common in PRP experiments, response times to task 1 were largely unaffected by this variation. The PRP effect was obtained despite careful control of strategic response deferment, and peripheral overlap of response modalities that may have artificially created performance costs in previous studies. Altogether, the present results show that dorsal processing is subject to the same capacity limitations that can almost universally be found with simple cognitive tasks.