At scales of 10 0 to 10 2 km, grain-size change in gravelly, alluvial systems is characterized by punctuated downstream fining. Significant lateral sediment inputs define a sequence of sedimentary links within which fluvial processes produce fining trends. Using a new set of surface grain-size data, eighteen such links along two Canadian gravel-bed rivers are examined. Negative exponential functions are found to be most appropriate for describing within-link grain-size changes. Development of a pragmatic means of predicting grain size is then pursued by searching for a means to relate model diminution coefficients to link attributes. Consideration of lithologically differentiated fining trends indicates that lithology plays an insignificant role in controlling fining rate. Examination of within-link longitudinal profiles indicates a reasonable relation between fining rate and the rate of change of channel slope. The predictive value of this relation is limited by the regional nature of the data upon which it is based and the relative difficulty of obtaining accurate gradient information. However, as previously noted for alluvial fans (although for different reasons), channel gradient is correlated with link length and a reasonable predictive tool is apparent in a relation between link length and diminution rate. The validity of the derived relation cannot be tested for want of a suitable data set. Several lines of evidence indicate that abrasion is unimportant as a fining mechanism on these rivers, and it is argued that this may be typical of sedimentary links. Fining rate must then be a function of the efficiency with which sorting processes operate, and it is suggested that this efficiency is dependent on aggradation rates associated with the lateral sediment influxes at the head and terminus of individual links.