Methods, apparatus and computer program products implement embodiments of the present invention that include configuring one or more storage devices as a plurality of physical storage units, each of the physical storage units having a storage granularity, and configuring, on the one or more storage devices, a thin provisioned storage pool having a physical number of the physical storage units and a logical number of logical storage units, the physical number being less than the logical number. Upon receiving a request to create a thick data volume having a requested number of the physical storage units, an available number of the physical storage units that are available in the thin provisioned pool can be identified. Upon determining that the requested number is less than the available number, the requested number of the physical storage units can be allocated, from the thin provisioned storage pool, to the thick data volume.