A data storage system employs a multi-level stack including a lower-deck file system and an upper-deck file system providing a file system interface to a file system consumer. The lower-deck file system presents a volume file to provide storage to the upper-deck file system. Storage is reserved to the upper-deck file system, and the volume file is fully provisioned so an out-of-space condition is not presented to the upper-deck file system. In an initial direct operating mode a block address in the lower-deck file system is obtained by a calculation from a corresponding block address in the volume file. Snapshots of a primary volume file are created and stored in respective snapshot volume files. The lower-deck file system transitions into a mapped mode using generally arbitrary mappings of block addresses of the primary volume file and snapshot volume files to obtain corresponding block addresses in the lower-deck file system.