Potential‐field (gravity) data are transformed into a physical‐property (density) distribution in a lower half‐space, constrained solely by assumed upper bounds on physical‐property contrast and data error. A two‐step process is involved. The data are first transformed to an equivalent set of line (2-D case) or point (3-D case) sources, using Euler’s homogeneity equation evaluated iteratively on the largest residual data value. Then, mass is converted to a volume‐density product, constrained to an upper density bound, by “bubbling,” which exploits circular or radial expansion to redistribute density without changing the associated gravity field. The method can be developed for gravity or magnetic data in two or three dimensions. The results can provide a beginning for interpretation of potential‐field data where few independent constraints exist, or more likely, can be used to develop models and confirm or extend interpretation of other geophysical data sets.