A nonlinear inversion scheme is described for the inversion of gravity data into a three-dimensional polyhedral model. As presented, the inversion scheme is quite general and could have application to a wide range of nonlinear problems. Constraints, in the form of independent geologic information, play an essential role in the analysis. The parameterization of the problem allows inclusion of exact linear constraints to limit possible model shapes and to construct multiple body models. It also significantly reduces the degrees of freedom in a problem and can help the stability of the iterative process. Plausibility constraints are used to limit the total departure of the solution from a starting model known to a specified level of confidence. The optimal trade-off between fitting noisy data and remaining close to a plausible starting model is determined empirically for each problem. The utility of the inversion scheme is illustrated with an example of estimating depth to bedrock from gravity data in Avra Valley, Arizona. The basin is modeled using three-dimensional polyhedra. The analysis indicates two deep portions in the elongate basin separated by a 0.8-km-deep saddle point. Uncertainties in the solution are estimated and the three controlling factors are independent control of depth to bedrock, data density, and basin depth. ¿ American Geophysical Union 1989