As part of a research program to develop gravity interpretation tools that can be merged with seismic techniques, a full 3-D complex structural inversion scheme for (possibly multibody) polyhedral models has been developed. The forward modeling algorithm was adopted from previous work. Because the inverse problem is generally very ill posed, several methods of regularizing the inversion were investigated and a combination of the most useful was adopted. The combination includes (i) a structured matrix formulation for the system equations, (ii) an analytical expression for the Jacobian calculation, (iii) first-derivative damping, (iv) a choice of damping parameter based on a variation of the trust region method, (v) a weighted scheme for parameter correction, and (vi) complete freezing of degrees of freedom found not to influence the gravity field significantly. This combination yields a robust inversion which was successfully demonstrated on data over the Galveston Island salt dome, offshore Texas. Variations of the technique should be applicable to magnetic data, which would make the method useful for mining problems and petroleum exploration settings involving volcanic structures.