An apparatus in an illustrative embodiment comprises at least one processing device comprising a processor coupled to a memory. The apparatus is configured to maintain a snapshot tree data structure having a plurality of volume nodes corresponding to respective ones of (i) a root volume and (ii) multiple snapshots related directly or indirectly to the root volume. The apparatus is further configured to determine a set of data descriptors for a given volume offset, to determine a set of reader volume nodes that are readers of a corresponding data item based at least in part on the set of data descriptors, to adjust one or more of the data descriptors in the set of data descriptors based at least in part on the set of reader volume nodes, and to reclaim storage space previously allocated to the data item responsive to the adjusting of the one or more data descriptors.