We have combined modeling and gravity inversion to estimate an overall smooth but locally discontinuous basement relief of a sedimentary basin. Through an initial global smoothness solution, the method indicates fault positions that may be accepted or modified. Then, the interpreter specifies the fault dip and a tentative fault slip, so the fault plane is fixed on the estimated relief. The segments of the current interpreted relief that are not accepted faults are estimated through smoothness inversion, and the response of the current estimated relief is computed. The slip of the fault being incorporated in the estimated relief is then modified interactively until the solution presents no side lobes about the fault extremes. The process is repeated for all faults. The iteration stops when the tentative solution becomes compatible with the geologic knowledge of the area and produces an acceptable data fit. The method was applied to data produced by a simulated graben defined by step faults dipping 60º and by inclined and arcuate terraces. The solution virtually coincided with the true source. The method’s ability in testing geologic hypotheses was demonstrated in gravity profiles across the Büyük Menderes Valley in west Turkey and the San Jacinto graben in southern California.