Constructing a general, three-dimensional model of the subsurface density distribution by minimum-structure, or Occam-style, inversion of gravity data has been practical now for several years. The usual approach is to seek a model that is simple in the sense of having the least amount of spatial variation while still reproducing the observations (hence the description “minimum-structure”). This has the advantage of generating models with few, if any, fictitious features. However, often the models produced bear only a gross, diffuse resemblance to geology. It has been recognized since the inception of the minimum-structure inversion technique that geological information can be incorporated by seeking a model that is simple in the sense of being as close as possible to a reference model while still fitting the observations. This is rarely done, often because insufficient geological information is available, or because inversion of geophysical data is no longer thought to be useful once a target has been found and drilling begun. Here we summarize a study demonstrating how models constructed using a minimum-structure inversion procedure can be influenced and constrained by reference models derived from downhole physical properties.