A method for data storage includes, in a memory that includes at least N memory units, each memory unit including memory blocks, defining superblocks, each superblock including a respective set of N of the memory blocks that are allocated respectively in N different ones of the memory units, such that compaction of all the memory blocks in a given superblock is performed without any intervening programming operation in the given superblock. Data is stored in the memory by computing redundancy information for a selected portion of the data, and storing the selected portion and the redundancy information in the N memory blocks of a selected superblock.