Downstream grain-size fining in stratigraphy is driven primarily by selective deposition of sediment, and the long-term efficiency of this process is determined by: (1) the magnitude and characteristics of the input sediment supply; (2) the spatial distribution of subsidence rate, which creates accommodation for sediment preservation; and (3) the dynamics of sediment transport and deposition. A key challenge is to determine how these first two factors control the caliber and spatial distribution of deposits over time scales of 10⁴–10⁶ yr without incorporating sediment transport details that are largely unknowable for time-averaged stratigraphy in the geological past. We address this using grain-size data collected from fluvial conglomerates in the Eocene Pobla Basin, Spanish Pyrenees, a synorogenic basin where the timing of sediment deposition is well-constrained; the sediment budget is closed; and good exposure enables time lines within stratigraphy to be picked out unambiguously. For successive stratigraphic horizons, downstream trends in grain size and composition are derived for basin-filling sediment-routing systems with length scales of 6 and 40 km, respectively. Our data show that the rate of grain-size fining varies over time and with system length and can be linked to changes in source area. These results are contrasted with grain-size data from the Antist Group, a 60-km-long Oligocene system that mantles the Southern Pyrenees, where very slow rates of grain-size fining on the wedge top of this fold-and-thrust belt are observed. We apply a self-similarity–based selective deposition model to quantify the competing controls of tectonic subsidence and sediment supply on derived grain-size trends, and model results are compared with independent constraints on the Eocene–Oligocene evolution of the Pyrenees. Our results suggest that it is now possible to invert time-averaged grain-size trends in stratigraphy to gain quantitative information on the geological boundary conditions governing the evolution of sedimentary basins.