The interpretation of gravity anomaly data suffers from a fundamental nonuniqueness, even when the solution set is bounded by physical or geologic constraints. Therefore, constructing a single solution that fits or approximately fits the data is of limited value. Consequently, much effort has been applied in recent years to developing inverse techniques for rigorous deduction of properties common to all possible solutions. To this end, Parker developed the theory of an ideal body, which characterizes the extremal solution with the smallest possible maximum density. Gravity ideal-body analysis is an excellent reconnaissance exploration tool because it is especially well suited for handling sparse data contaminated with noise, for finding useful, rigorous bounds on the infinite solution set, and for predicting accurately what data need to be collected in order to tighten those bounds. We present a practical three-dimensional gravity ideal-body computer code, IDB, that can optimize a mesh with over 10 5 cells when used on a CRAY computer. Using actual gravity data, we use IDB to produce ideal-body tradeoff curves that bound the solution set and show how to restrict the bound on the solution further by applying geologic and geophysical data to the tradeoff curves. As an example, we compare two-dimensional and three-dimensional ideal-body results from a study of a positive anomaly associated with the Lucero uplift located on the western flank of the Rio Grande rift in New Mexico.