Salt diapirs in the Norwegian Danish Basin are characterized by the occurrence of marked angular unconformities which dip towards the diapirs. These unconformities developed above salt pillows, showing that the pillows grew close to the surface, or even reached the surface, in the time interval predating diapir formation. By contrast, the unconformities above present-day pillows show that these pillows have never reached close to the surface, strongly suggesting that pillow growth to "near unroofing" was a necessary condition for a transition to diapirism. Evidence from pillows indicates that unroofing in some cases was an asymmetric process involving growth of the pillow on the footwall side of a fault which soles out on the top surface of the salt. A consequence of this mechanism is that a separate stage of salt structure growth, with a combination of both pillow and diapir features, must be included in a general model for the "classical" Zechstein basin salt structures.