Trajectories of goal-directed movements are less curved for movements over a surface (constrained) than for movements in empty space (unconstrained). To study whether this difference arises from feeling the surface slip across the skin or having to control the movements in a third dimension, we manipulated the available tactile information and the compliance of the surface. Participants were instructed to make straight movements towards haptic targets in the mid-sagittal plane. We found that constrained movements were less curved than unconstrained movements. The reduction of curvature was also visible with strongly reduced tactile information and for very compliant surfaces, so feeling the surface slip across the skin and having to control the movements in the third dimension are not critical. The reduced curvature when moving over a surface might arise from the extra information that the surface gives about the third dimension or from the extra information about the direction of the movement provided by the additional force needed to overcome friction.