Variability in behavior can be a manifestation of unwanted noise. However, variability can also reflect exploration, and benefit learning. For example, it has been shown that inter-individual differences in motor learning can be partly explained by differences in movement variability at baseline. Here, we examined whether permitting vs. constraining movement variability via target shape alters motor learning rate in one and the same individual. Healthy young subjects reached to visual targets in 2D space with their unseen hand. During an initial priming phase, the shape of targets allowed for movement variability either in direction (arc-shaped targets), or, in a separate session, in extent (radially oriented line-shaped targets), while requiring highly precise movements in the other spatial dimension, respectively. In subsequent test phases in each session, we quantified the rate of (single-trial) motor adaptation to visuomotor perturbations along these two spatial dimensions (rotation and gain). During priming, we observed higher variability in movement direction for arc-shaped targets, compared to radial line-shaped targets, and vice versa for variability in movement extent. As predicted, participants adapted more to a visuomotor rotation following priming with arc-shaped targets, compared to radial line-shaped targets, and vice versa for adaptation to a change in visuomotor gain. This effect was prominent in the part of the examined workspace where variability in initial movement trajectories was highest, suggesting high planning noise. Our results suggest that workspace redundancy can modulate motor adaptation in a spatially specific manner, however, this modulation may depend on the level of planning noise.