We have analyzed the way in which simulated textures made of random dots influence visual suprathreshold color tolerances. We considered 32 textures created by a systematic variation of the following variables: size, number, and color of the dots. Each texture was mapped on the five centers recommended by the International Commission on Illumination (CIE) in 1978 [Color Res. Appl.3, 149 (1978)]. A panel of five experienced observers determined the experimental tolerances using a CRT color monitor by the method of adjustment. At our observation distance, neither small differences in dot size (1 or 4 pixels) nor sparse number of dots (less than 20% of the surface of the sample) changed the tolerances found for homogeneous samples. For the textures that led to statistically significant differences with respect to homogeneous samples, the parametric factors of CIEDE2000 and CIE94 color-difference formulas were fitted. These simulated textures consistently reduced the color difference perceived in a pair or, equivalently, increased the tolerances, mainly (but not only) lightness tolerance. The results demonstrate that it is not simple to provide a unique set of parametric factors for all the potential textures.