We have studied a gabbro intrusion in northern Sweden, using 3D inversion of airborne magnetic data, ground-based gravity data, and petrophysical measurements on outcrop samples. Gabbro intrusions are of interest because they are potential hosts of Cu-Ni and platinum group element mineralization. We developed a joint inversion algorithm and applied it to both potential-field data sets to obtain spatial distributions of density and magnetic susceptibility. The distributions were coupled through a nonrigidly enforced parameter relationship determined from the petrophysical samples. We managed the problem of balancing the influence of the two data sets by a novel adaptive reweighting scheme that enforced the discrepancy principle for each data set independently. We demonstrated in tests with synthetic data that neither individual nor joint inversions gave reliable estimates for the depth extension of the intrusive body, the near-surface details, or any complex geometrical features. However, the joint inversion improved the image of the interface between the intrusion and the surrounding rocks and revealed that the density and susceptibility models satisfied the observed petrophysical relationship, which, in turn, caused the structures in the models to align. The geometry of the intrusion was an intrinsic result of the inversion, based on the two distinct petrophysical trends for the gabbro and the surrounding rocks. The inferred shape was simple and concise, and was therefore a useful and testable hypothesis about the subsurface geology that was in agreement with both potential-field data sets and the petrophysical information.