A method for data storage includes, in a memory that includes multiple memory blocks, specifying at a first time a first over-provisioning overhead, and storing data in the memory while retaining in the memory blocks memory areas, which do not hold valid data and whose aggregated size is at least commensurate with the specified first over-provisioning overhead. Portions of the data from one or more previously-programmed memory blocks containing one or more of the retained memory areas are compacted. At a second time subsequent to the first time, a second over-provisioning overhead, different from the first over-provisioning overhead, is specified, and data storage and data portion compaction is continued while complying with the second over-provisioning overhead.