Tactile fingertip devices of vertically moving tactors have two important design parameters that significantly affect physical feedback and human tactile perception: tactor size and tactor density. However, there are a limited number of research studies that have evaluated the effect of these parameters on human tactile perception. This paper investigated the influence and interaction of these two parameters on a discrimination task. The task consisted of discriminating the spatial-period of sinusoidal gratings through the use of passive-guided touch. In two complementary experiments 40 participants performed the discrimination task under two different tactile conditions: (I) using direct bare fingertip sensing (baseline condition), and (II) using tactile displays with different tactor spacings and diameters. In both experiments differences between and within subjects were considered for Condition II, and for all test conditions the spatial-period Weber fraction for each participant was measured. Results from both experiments were consistent in indicating that tactile performance improves as tactor spacing is decreased and tactor diameter is increased. However, tactor spacings below 1.1 mm might not result in any significant further improvement. The findings of this study might help designers to choose design parameters for tactile displays based upon the cost-benefit of tactor density versus perceptual performance.