One facet of the debate about the hypothesis of equal mobility of all grain sizes in a mixture is that equal mobility seems contrary to field evidence for selective deposition as an important mechanism of downstream fining. We argue that regardless of the ultimate outcome of the equal mobility debate, variability in local mean grain size across a reach can give rise to strong selective deposition even if locally equal mobility is satisfied exactly. We consider a system in which the sediment is arranged into locally well mixed zones (“patches”) whose mean grain size varies randomly across the reach. We assume that the shear stress is randomly distributed with a mean value near the critical value for the reach‐averaged median size, that the variance in stress scales with the variance in grain size, and that the development of fine patches in areas of high shear stress is supply limited. The main controls on fining rate are then the ratio of mean stress to critical stress for the section‐averaged mean grain size and the ratio of the patch standard deviation (assumed constant) to the standard deviation of patch means. In addition, in any system in which fining occurs by selective transport and deposition, the fining rate is strongly influenced by the spatial distribution of deposition rate.