We studied human haptic perception of sine-wave gratings. In the first experiment we measured the dependence of amplitude detection thresholds on the number of cycles and on the wavelength of the gratings. In haptic perception of sine-wave gratings, the results are in agreement with neural summation. The rate at which detection thresholds decrease with increasing number of cycles is much higher than can be accounted for by probability summation alone. Further, neural summation mechanisms describe the detection thresholds accurately over the whole spatial range probed in the experiment, that is wavelengths from 14 mm up to 225 mm. Earlier, we found a power-law dependence of thresholds on the spatial width of Gaussian profiles (Louw et al, 2000 Experimental Brain Research 132 369-374). The current results extend these findings; the power-law dependence holds not only for Gaussian profiles, but also for a broad range of sine-wave gratings with the number of cycles varying between 1 and 8. Haptic perception involves tactual scanning combined with an active, dynamic exploration of the environment. We measured characteristics of the velocity and force with which stimuli were scanned while performing a psychophysical task. One particularly surprising finding was that, without being instructed, participants maintained an almost constant scanning velocity during each 45-min session. A constant velocity in successive trials of the experiment might facilitate or even be necessary for discrimination. Further, a large systematic dependence of velocity on scanning length was found. An eightfold increase in scanning length resulted in about a fourfold increase in scanning velocity. A second experiment was conducted to study the influence of scanning velocity on psychophysical detection thresholds. This was done by systematically imposing specific scanning velocities to the participants while the thresholds were measured. The main result of the second experiment was that psychophysical detection thresholds are constant over a relatively broad range of scanning velocities.