Regional grain size trends in fluvial successions can reveal important information regarding the dynamics of sediment routing systems. Self-similar solutions for down-system grain size fining have recently been proposed to explore how key variables, such as the spatial distribution of deposition, sediment discharge, and sediment supply characteristics, control spatial distribution of grain size in fluvial successions over time scales of 104–106 years. We explore the sensitivity of these solutions to changes in key variables and assess their applicability to ancient fluvial successions. Several sensitivity analyses are presented to investigate the relative control of the key model variables on the spatial pattern of down-system grain size fining in fluvial successions. Sensitivity analyses demonstrate that (1) an increase in the initial value of sediment discharge to a basin causes a decrease in the rate of grain size fining in fluvial successions, an effect that becomes nonlinear for large values of initial sediment discharge; (2) a short-wavelength/high-amplitude subsidence regime generates a greater rate of down-system grain size fining and a long-wavelength/lower-amplitude subsidence regime generates a lesser rate of down-system grain size fining in fluvial successions; and (3) an increase in the spread of grain sizes in the sediment supply generates a greater rate of down-system grain size fining. We apply this modeling technique to grain size data sets collected from two time surfaces within conglomerates of the Upper Eocene Montsor Fan Succession of the Pobla Basin, Spanish Pyrenees. These data sets exhibit approximately self-similar grain size distributions; further, the observed increase in down-system grain size fining associated with smaller depositional system lengths provides support for the application of self-similar solutions to fluvial successions. By applying these solutions to carefully collected grain size data from fluvial successions, we are able to relate explicitly the initial grain size supplied to the system, the spatial distribution of subsidence and the sediment discharge into the basin to the rate of grain size fining in fluvial successions. This method thus offers a powerful means of elucidating sediment routing system dynamics over time.