Stochastic inversion for flexural loads and flexural rigidity of the continental elastic layer can be accomplished most effectively by using the coherence of gravity and topography. However, the spatial resolution of coherence analysis has been limited by use of two-dimensional periodogram spectra from very large (>105 km2) windows that generally include multiple tectonic features. Using a two-dimensional spectral estimator based on the maximum entropy method, the spatial resolution of flexural properties can be enhanced by a factor of 4 or more, enabling more detailed analysis at the scale of individual tectonic features. This new approach is used to map the spatial variation of flexural rigidity along the Basin and Range transition to the Colorado Plateau and Middle Rocky Mountains physiographic provinces. Large variations in flexural isostatic response are found with rigidities ranging from as low as 8.7¿1020 N m (elastic thickness Te=4.6 km) in the Basin and Range to as high as 4.1¿1024 N m (Te=77 km) in the Middle Rocky Mountains. These results compare favorably with independent determinations of flexural rigidity in the region. Areas of low flexural rigidity correlate strongly with areas of high surface heat flow, as is expected from the contingence of flexural rigidity on a temperature-dependent flow law. Also, late Cenozoic normal faults with large displacements are found primarily in areas of low flexural rigidity, while deformation fronts of Mesozoic/Tertiary overthrusts occur 0 to 100 km east of the low-rigidity region. The highest flexural rigidity is found within the Archean Wyoming craton, where evidence suggests that deeply rooted cratonic lithosphere may play a role in determining the distribution of tectonism at the surface. ¿ American Geophysical Union 1994