Incised valleys are critical stratigraphic features for unraveling long-term Earth-surface processes and depositional history, and commonly exhibit stratigraphic attributes that make them desirable fluid reservoirs. While there is much descriptive documentation on architecture of incised-valley fills and paleoenvironmental regimes, relatively little work has focused on quantitative modeling of the dynamics of incised-valley evolution. Here we use well-constrained observations of incised valleys in experiments and the field to explore controls on valley geometry and develop a simple valley model to quantify the primary dynamics of incised-valley evolution. We document a strong tendency for incised valleys to widen downstream independent of the details of the relative base-level curve or initial surface profile, due primarily to the effects of increased sediment flux. This is in general agreement with measurements of experimental and natural incised valleys, though the degree of widening is less in natural systems due to greater sidewall resistance and smaller water discharge (relative to valley size). A first-order model of incised-valley evolution highlights three important trends: valley aggradation and widening; valley incision and widening; and valley incision and narrowing. The model reproduces the primary geometric responses to valley formation as measured from experiments: valley width and depth both increase in response to increases in (1) local relative base-level fall and (2) the initial offshore water depth. Finally, we generalize the first-order controls on valley geometry via dimensional analysis to show that long-term valley narrowing is not readily produced from relative base-level fall alone.