The assumption that particle-size distribution (PSD) in Mil may often be described as approximately lognormal was tested and found to be inadequate for many textures. With texture specified by mass fractions of clay, silt, and sand in a texture triangle, it is shown that the unimodal lognormal distribution can describe PSD, to within chosen degrees of approximation, over only about half of the USDA triangle. “Disallowed” textures are excluded primarily by their width of textural spread, requiring excessive undersize (d< 0.02 μm) or oversize (d > 2 mm) tails in the distribution. They would require alternative distribution functions (e.g., skewed unimodal, bimodal). Equations are given for the two lognormal (size “mean” and “spread”) parameters for eligible textures within the “allowed” triangle area. The theory enables mapping between triangles of different texture systems (e.g., USDA, International) for eligible textures. The rationale of predicting soil properties from two-parameter textural representations is discussed. Two. classes of property are identified, according to their likely optimal regression parameters: (1) properties dominated by the clay or colloidal fraction (mass-fraction parameters, only two of which are independent) and (2) properties dependent on overall particle- or poresize distributions (transformed, size-distribution parameters). The lognormal parameters derived here offer a new basis for regression of class 2 properties for eligible textures.