We report sensitivity tests on a numerical model of the development of downstream fining by size-selective transport and deposition above a base level in a gravel-bed river with no lateral inputs of water or sediment. Strong fining requires deposition mainly to the surface; otherwise, its amount and streamwise distribution are not highly sensitive to any single factor but vary somewhat with hiding factor, excess shear stress, and bed sorting. Low initial concavity inhibits fining, but different higher concavities generate fairly similar fining profiles. Lower sediment supply leads to a coarser bed with less fining, but there is no simple relationship between fining and aggradation rate. The rate of development of fining is sensitive to all these factors but is always rapid initially, followed by a far slower approach towards final equilibrium. Surface grain size adjustment is potentially an important degree of freedom in river response to any environmental change or human impact which causes overloading.¿ 1997 American Geophysical Union