A data storage management system is enhanced to accommodate, and moreover to optimize, the storing and retention of deduplicated secondary copies at write-once read-many (WORM) enabled storage platforms. Enhancements include without limitation: user interface (UI) options to enable WORM functionality for secondary storage, whether used for deduplicated or non-deduplicated secondary copies; enhancements to secondary copy (e.g., deduplication copy, backup) operations; and pruning changes. The storage manager is generally responsible for managing the creation, tracking, and deletion of secondary copies, with and without deduplication. Media agents that store secondary copies to and prune them from the WORM-enabled storage platforms also are enhanced for communicating and interoperating with both bucket-level and object-level WORM-enabled storage platforms to implement the features disclosed herein.