An illustrative approach to managing snapshots streamlines how and when snapshots are generated in a storage management system, such that fewer snapshots may be generated without diminishing the scope of data protection. A novel unified-snapshot storage policy may govern snapshots for any number of subclients. A unified-snapshot job based on the unified-snapshot storage policy enables the illustrative storage management system to automatically discover relevant components and generate at most one snapshot per target logical unit number (“LUN”) in a storage array. Each snapshot may comprise the data of any number of subclients and/or clients in the storage management system. Accordingly, one unified-snapshot job may yield a minimum but sufficient number of snapshots comprising data of all subclients associated with the governing unified-snapshot storage policy. An enhanced storage manager may manage the unified-snapshot jobs. One or more enhanced media agents and/or data agents may participate in the unified-snapshot jobs and in subsequent cataloguing of the snapshots.