This work uses sandbox analogue models to analyze the formation and subsequent inversion of a decoupled extensional system comprised of two segmented half-grabens with thick early syn-rift salt. The segmented half grabens strike perpendicular to the direction of extension and subsequent shortening. Rifting created first a basement topography that was infilled by model salt, followed by a second phase of extension and sedimentation, followed afterwards by inversion. During the second phase of extension, syn-rift syncline minibasins developed above the basement extensional system and extended beyond the confines of the fault blocks. Sedimentary downbuilding and extension initiated the migration of model salt to the basement highs, forming salt anticlines, reactive diapirs, and salt walls perpendicular to the direction of extension, except for along the transfer zone where a slightly oblique salt anticline developed. Inversion resulted in decoupled cover and basement thrust systems. Thrusts in the cover system nucleated along squeezed salt structures and along primary welds. New primary welds developed where the cover sequence touched down on basement thrust tips due to uplift, salt extrusion, and syn-contractional downbuilding caused by loading of syn-contractional sedimentation. Model geometries reveal the control imposed by the basement configuration and distribution of salt in the development of a thrust front from the inversion of a salt-bearing extensional system. In 3D, the interaction of salt migrating from adjacent syn-rift basins can modify the expected salt structure geometry, which may in turn influence the location and style of thrust in the cover sequence upon inversion. Results are compared to the northern Lusitanian Basin, offshore Portugal and the Isàbena area of the South-Central Pyrenees, Spain.