A method for data storage includes defining, in a memory that includes multiple analog memory cells, an erased state, a set of non-erased programming states and a partial subset of the non-erased programming states. Data is initially stored in a first group of the analog memory cells by programming each of at least some of the memory cells in the first group from the erased state to a respective non-erased programming state selected from the set of non-erased programming states. After initially storing the data, a second group of the analog memory cells, which potentially cause interference to the first group, is programmed. After programming the second group, the first group is selectively re-programmed with the data by repeating programming of only the memory cells in the first group whose respective programming states belong to the partial subset.