Salt ‘withdrawal’ sedimentary minibasins, common features of salt tectonic provinces, are typically subcircular or polygonal, 10–30 km in diameter, and contain as much as 10 km of sediment above evaporite that has been expelled into surrounding diapiric structures. The early development of minibasins typically is not buoyancy driven (Rayleigh-Taylor instability) because thin sediment overburden is usually less dense than salt (strictly, halite) or other evaporites. We analyze an alternative mechanism that applies in compressional regimes involving sedimentation onto salt, lateral flow and shortening of sediment and salt to form viscous pressure ridges (VPRs) (the key process). Loading by sediment ponded between VPRs provides a positive feedback that grows the pressure ridges. We show using lubrication theory and numerical models that this mechanism quantitatively solves the enigma and grows minibasins until the compacting sediment is sufficiently thick and dense for Rayleigh-Taylor instabilities to take over.