This paper develops an inversion technique for static surface displacements associated with shallow faulting and applies the method to geodetic observations of the Borah Peak, Idaho, earthquake (M0=7.3) of October 28, 1983. This technique improves upon classical, uniform slip planar (USP) models by admitting earthquake faults which are curved and contain variable slip. By summing elemental point sources, employing a gradient strategy with positivity constraints, and combining both geodetic and surface scarp height data, we can now resolve fault orientation, dimension, shape, and slip distribution. Large formal misfits to the geodetic data and disagreements in observed surface scarp locations found with the best USP fault are eliminated in variable slip planar (VSP) models. The best VSP fault reaches to 18 km depth in the southeast but only to 3 km depth in the northwest. Surface slip and slip at depth are poorly correlated in the VSP model. In fact, toward the southeast, slip at depth extends 13 km beyond the terminus of the fault's surface expression. Three or four knots of concentrated slip are found in VSP models. These knots are 3-6 km in dimension and may represent the breaking of asperities. To test for listric-like behavior of the Borah Peak fault, we considered all possible variable slip listric (VSL) faults of parabolic shape. The best VSL model has a slight downward curvature; however, it does not fit the data significantly better than VSP models. The geodetic measurements do not support significant listric curvature at depths shallower than 20 km. Our techniques permit the calculation of sensitivity kernels for surface displacement. These functions explicitly reveal fault locations where a certain geodetic measurement is most sensitive. For faults like Borah Peak, a surface measurement at point r samples slip to a depth roughly equal to the distance from r to the fault trace. Consequently, near fault bench marks and surface scarp height measurements are very weak constraints on slip at depth. We feel that variable slip fault models will allow significant new interpretations to be drawn from the geodetic data pool concerning the physics of earthquakes and their potential hazard.