We apply the two-dimensional strain rate inversion algorithm described in the companion paper to five sedimentary basins located world wide. This general algorithm makes no assumptions about the number, duration, or intensity of rifting episodes within a basin. Instead, the distribution of strain rate is allowed to vary smoothly through space and time until the misfit between observed and predicted stratigraphy is minimized. Potentially important two-dimensional effects such as lateral heat flow and elastic thickness have been incorporated. In each case, observed subsidence profiles can be automatically and accurately fitted. The calculated distributions of strain rate are corroborated by independent information about the number and duration of rifting episodes. Peak strain rate estimates are comparable to present-day measurements in actively extending basins such as the Aegean Sea and the Basin and Range Province. Temporal and spatial strain rate patterns from a large number of sedimentary basins in diverse settings will help to constrain the dynamical evolution of thinning continental lithosphere. In all five sedimentary basins, the smallest acceptable misfit is achieved when the elastic thickness is less than 2--4 km. This surprising result indicates that the lithosphere beneath sedimentary basins remain weak during and after rifting. It also underscores the importance of inverting data sets so that the existence, uniqueness, and resolution of solutions can be analyzed. Our two-dimensional approach is one small step toward a generalized three-dimensional inverse model of sedimentary basins.