The concept of South America and Africa as rigid continents during the formation, growth and motion of their respective plates has frustrated reconstruction of a tight, geologically economic fit between these two fragments in their Gondwana framework. We recognize that (1) internal strains released during and following Gondwana break-up have distorted their actual shapes within Gondwana and (2) these two continents comprise mosaics of smaller microblocks, or platelets, of relatively undistorted Precambrian terrains that experienced modest, episodic relative motions along rift zones that separate them. This permits a fresh approach to quantitative reconstructions of palaeo-continents. Former geological ties forged at the time of Gondwana amalgamation, now exposed at the continental margins of the South Atlantic as piercing points, provide robust anchors for new paleo-cartographic experiments. We present two new tectonic maps of the Brasiliano and Pan-African structures of West Gondwana on which we identify ten piercing points that, if re-joined simultaneously, could facilitate quantification of a well-substantiated Gondwana fit and help retrace the evolution of its continental margins with greater accuracy than has been achieved until now. This has significant bearing on understanding the origin and evolution of passive continental margins, and the geodynamics of Gondwana break-up.