A storage system comprises a plurality of storage devices and an associated storage controller. The storage controller is configured to receive a request to copy a first range of logical addresses to a second range of logical addresses, determine at least one physical block of the storage devices to which the first range of logical addresses is mapped, map the second range of logical addresses to the determined at least one physical block, and add at least one content-based signature associated with the determined at least one physical block to a pending increment data structure that includes content-based signatures corresponding to physical blocks for which an increment of an associated reference count is pending. The storage controller is further configured to execute a pending increment of a reference count associated with a given physical block corresponding to at least one of the content-based signatures in the pending increment data structure.