1. A method for data storage, comprising: in a first programming phase, storing first data in a first plurality of analog memory cells, wherein storing the first data includes programming each analog memory cell of the first plurality of analog memory cells to a given one of a set of initial programming levels dependent upon the first data; and in a second programming phase, that is subsequent to the first programming phase, storing second data in the plurality of analog memory cells wherein storing the second data includes: reading the stored first data in each analog memory cell of the plurality of analog memory cells; identifying, dependent upon the read stored first data, analog memory cells of the first plurality of analog memory cells that were programmed, in the first programming phase, to a level included in a designated partial subset of the set of initial programming levels; and programming at least one of the identified analog memory cells to a given one of one or more additional programming levels dependent upon the second data, wherein each one of the one or more additional programming levels is different from each one of the set of initial programming levels.