Participants perceive a distal surface texture to be of a certain roughness despite being explored in different ways: by active or passive touch or at different speeds. Understanding the basis and extent of this roughness constancy is an important theoretical goal. The literature suggests that it may stem from how one class of cutaneous afferents codes texture element spacings. In different experiments using raised dot surfaces, we investigated participants? abilities to discriminate spatial density gradients of different directions and magnitudes. This was done under conditions where fingers changed and where performance over extended practice could be observed. The data confirm that perceptual constancy is a feature of haptic texture perception but we identify a subtle bias in perception and we find evidence that practice, even without feedback as to accuracy, can enable even subtle spatial changes to be perceived. We consider these data in terms of models of haptic texture perception and perceptual learning.