Several recent studies have shown general consistency of fluvial denudation rates over long time periods, or historical and contemporary sediment yields of the same general magnitude as sediment yields or accumulation rates over geologic time. This consistency of fluvial sediment export from some drainage basins, despite substantial climate, hydrological, ecological, base level, and other environmental changes, suggests that long-term sediment yields may be controlled by factors that are independent of and overwhelm environmental changes (e.g. tectonics), or that the fluvial sediment system is at some level dynamically stable. The latter is explored via a model based on the notion that all debris produced by weathering within a drainage basin over any time period is either retained as part of the regolith, transported out of the basin as solid or dissolved sediment yield, or stored as alluvium within the fluvial system. This system is dynamically stable if alluvium is always potentially available for transport; e.g. to be converted to yield, and if regolith development exerts a negative feedback on weathering rates. This supports the argument that the long-term consistency of sediment yields (where it exists) may be attributable to the storage and remobilization of alluvium, which buffers the system against environmental change. Environmental changes are manifested primarily in reorganizations within the fluvial sediment system, such as variations between net increases and decreases in alluvial storage, and changes in the spatial locus of deposition. These ideas are illustrated and tested using data from the lower Trinity River in southeast Texas.