A file server maintains a production file system supported by a clone volume, and multiple snapshot file systems supported by respective save volumes in a snapshot queue. Before a data block is modified for the first time after creation of the youngest snapshot, the data block is copied from the clone volume to the save volume of the youngest snapshot. A bit map indicates the blocks that have already been copied, and a block map shows the save block address for each corresponding clone block address. When a new snapshot is created, the bit and block maps are converted to a hash index that is kept linked to the save volume of what had been the youngest snapshot. When other than the oldest snapshot file system is deleted, the respective save volume is retained as a hidden object until it becomes the oldest save volume.