The Newfoundland-Iberia rift, which includes the Lusitanian Basin (LB), has been considered the archetype of a magma-poor rift, but its main steps are still debated. The new data reported here indicate that the LB’s eastern border comprises two contrasting types of contact between continental sediments and Variscan basement: major angular unconformity and master bounding fault. The unconformable contact could mean a pre-rift sag basin, or a syn-rift half-graben with flexural boundary in the E. However, given that newly recognized master NW-SE to NNW-SSE bounding faults displace the red continental deposits and basal unconformity by hundreds of meters, we infer that the master bounding fault is Alpine and displaces the base of a previous sag basin. In the case of unconformable contact and sag basin, the age of the red continental deposits would be older than the currently attributed Late Triassic age, and represent the missing Late Variscan denudation molasse. It seems therefore that the LB could be a rift basin underlain by an older and smaller sag basin. Later, Pangaea rifting produced a full graben, the LB, bounded to the east by a newly mapped master fault reactivating a major Variscan shear zone in the northern half of the Lusitanian Basin. A similar development of composite basins can be found in NE Brazil, where some Mesozoic intracontinental basins also show evidence of two-stage basin formation, an early sag (Palaeozoic) and a later rift (Mesozoic).