A technique for managing data received into a cache operates in cycles. To process a current batch of compressed blocks during a current cache processing cycle, a storage system obtains a new mapping structure and a new segment of contiguous storage space. If the system can place some of the current batch of compressed blocks into previously-allocated space, the system does so and partially populates the new mapping structure with entries for mapping the other compressed blocks that were not placed. The system then asserts a hold on the new mapping structure, so that the mapping structure is retained in cache at the end of the current cache processing cycle, and more completely populates the new mapping structure with entries for other compressed blocks during a later cache processing cycle before releasing the hold.