Edges are fundamental properties of our environment and the objects we interact with. There is a lack of research on the haptic perception of edges, especially the sharpness of an edge. Skinner et al. [2013 PLoS ONE, 8(9): E73283] found that haptic discriminability of sharpness was clearly superior when using a relatively unrestrained, free exploration strategy compared with a static single touch strategy. In the free exploration condition two distinct movement patterns were frequently used by participants: a proximal-distal movement of the fingerpad across the test edge and a medial-lateral movement of the fingerpad along the test edge. Here, using the same stimuli and two-alternative forced-choice method of constant stimuli as Skinner et al. (2013), we demonstrate that a proximal-distal movement results in substantially lower sharpness discrimination thresholds than a medial-lateral movement. The underlying neurophysiology and implications for the design of haptic displays are considered.