Discrepancies among previous models of the geometry of the Albuquerque Basin motivated us to develop a new model using a comprehensive approach. Capitalizing on a natural separation between the densities of mainly Neogene basin fill (Santa Fe Group) and those of older rocks, we developed a three-dimensional (3D) geophysical model of syn-rift basin-fill thickness that incorporates well data, seismic-reflection data, geologic cross sections, and other geophysical data in a constrained gravity inversion. Although the resulting model does not show structures directly, it elucidates important aspects of basin geometry. The main features are three, 3–5-km-deep, interconnected structural depressions, which increase in size, complexity, and segmentation from north to south: the Santo Domingo, Calabacillas, and Belen subbasins. The increase in segmentation and complexity may reflect a transition of the Rio Grande rift from well-defined structural depressions in the north to multiple, segmented basins within a broader region of crustal extension to the south. The modeled geometry of the subbasins and their connections differs from a widely accepted structural model based primarily on seismic-reflection interpretations. Key elements of the previous model are an east-tilted half-graben block on the north separated from a west-tilted half-graben block on the south by a southwest-trending, scissor-like transfer zone. Instead, we find multiple subbasins with predominantly easterly tilts for much of the Albuquerque Basin, a restricted region of westward tilting in the southwestern part of the basin, and a northwesterly trending antiform dividing subbasins in the center of the basin instead of a major scissor-like transfer zone. The overall eastward tilt indicated by the 3D geophysical model generally conforms to stratal tilts observed for the syn-rift succession, implying a prolonged eastward tilting of the basin during Miocene time. An extensive north-south synform in the central part of the Belen subbasin suggests a possible path for the ancestral Rio Grande during late Miocene or early Pliocene time. Variations in rift-fill thickness correspond to pre-rift structures in several places, suggesting that a better understanding of pre-rift history may shed light on debates about structural inheritance within the rift.