This work studies the preattentive discrimination of achromatic textures composed of mixtures of different (Weber) contrasts. These textures differ not at all in local spatial structure, but only in the relative proportions of different contrasts they comprise. It is shown that, like chromatic discrimination, preattentive discrimination of such textures is three-dimensional. The current results do not uniquely determine the characteristics of the three texture filters mediating human discrimination of these textures; they do, however, define the space of textures with 4th-order polynomial histograms to which human vision is sensitive. Three real-valued functions of contrast that collectively capture human sensitivity to the textures in this space are presented.