An underlying physical volume of a storage system is an aggregate having a plurality of storage devices. The aggregate has its own physical volume block number (pvbn) space. A file system layout apportions the underlying physical volume into a plurality of virtual volumes of the storage system each having a virtual volume identification (vvid). Each virtual volume has its own virtual volume block number (vvbn) space. The block allocation structures of a virtual volume are sized to the virtual volume, and not to the underlying aggregate, to thereby allow operations that manage data served by the storage system (e.g., snapshot operations) to efficiently work over the virtual volumes. Each storage block in a virtual volume is identified by the triplet: pvbn, vvid, and vvbn.