| In this paper, we present the results of experiments that explore the ability of the human fingertip to detect haptically simulated first-order and second-order surface discontinuities. A single finger, planar motion fingertip haptic display (FHD) developed at the University of Washington was used by multiple test operators to kinesthetically trace haptically simulated surfaces under a variety of treatment conditions. Experiment variables included the magnitude and type of discontinuity, as well as the stiffness and damping terms used in the haptic simulation algorithm. Test operators were asked to haptically locate a discontinuity on a simulated surface for each treatment condition with the location accuracy being used as the experiment performance metric. The results reveal how the surface discontinuity detection ability is degraded by control gains that are either too low or too high, indicating that a given haptic simulation system may have an optimum set of control gains that will yield the best performance for this type of task.