Friction modulation technology enables the creation of textural effects on flat haptic displays. However, an intuitive and manageably small design space for construction of such haptic textures remains an unfulfilled goal for user interface designers. In this paper, we explore perceptually relevant features of fine texture for use in texture construction and modification. Beginning with simple sinusoidal patterns of friction force that vary in frequency and amplitude, we define irregularity, essentially a variable amount of introduced noise, as a third building block of a texture pattern. We demonstrate using multidimensional scaling that all three parameters are scalable features perceptually distinct from each other. Additionally, participants’ verbal descriptions of this 3-dimensional design space provide insight into their intuitive interpretation of the physical parameter changes.