Goal-directed movements, such as reaching out to grasp an object, are necessarily constrained by the spatial properties of the target such as its size, shape, and position. For example, during a reach-to-grasp movement, the peak width of the aperture formed by the thumb and fingers in flight (peak grip aperture, PGA) is linearly related to the target's size. Suppressing vision throughout the movement (visual open loop) has a small though significant effect on this relationship. Visual open loop conditions also produce a large increase in the PGA compared to when vision is available throughout the movement (visual closed loop). Curiously, this differential effect of the availability of visual feedback is influenced by the presentation order: the difference in PGA between closed- and open-loop trials is smaller when these trials are intermixed (an effect we have called 'homogenization'). Thus, grasping movements are affected not only by the availability of visual feedback (closed loop or open loop) but also by what happened on the previous trial. It is not clear, however, whether this carry-over effect is mediated through motor (or sensorimotor) memory or through the interference of different task sets for closed-loop and open-loop feedback that determine when the movements are fully specified. We reasoned that sensorimotor memory, but not a task set for closed and open loop feedback, would be specific to the type of response. We tested this prediction in a condition in which pointing to targets was alternated with grasping those same targets. Critically, in this condition, when pointing was performed in open loop, grasping was always performed in closed loop (and vice versa). Despite the fact that closed- and open-loop trials were alternating in this condition, we found no evidence for homogenization of the PGA. Homogenization did occur, however, in a follow-up experiment in which grasping movements and visual feedback were alternated between the left and the right hand, indicating that sensorimotor (or motor) memory can operate both within and between hands when the response type is kept the same. In a final experiment, we ruled out the possibility that simply alternating the hand used to perform the grasp interferes with motor or sensorimotor memory. We did this by showing that when the hand was alternated within a block of exclusively closed- or open-loop trials, homogenization of the PGA did not occur. Taken together, the results suggest that (1) interference from simply switching between task sets for closed or open-loop feedback or from switching between the hands cannot account homogenization in the PGA and that (2) the programming and execution of grasps can borrow not only from grasping movements executed in the past by the same hand, but also from grasping movements executed with the other hand.