1. A method for data storage, comprising: in a memory that includes multiple analog memory cells, defining an erased state, a set of non-erased programming states and a partial subset of the non-erased programming states; initially storing data 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, programming a second group of the analog memory cells, which potentially cause interference to the first group; and after programming the second group, selectively re-programming the first group with the data by repeating programming of only the memory cells in the first group whose respective programming states belong to the partial subset.