A method for operating a memory (36) includes storing data in a plurality of analog memory cells (40) that are fabricated on a first semiconductor die by writing input storage values to a group of the analog memory cells. After storing the data, multiple output storage values are read from each of the analog memory cells in the group using respective, different threshold sets of read thresholds, thus providing multiple output sets of the output storage values corresponding respectively to the threshold sets. The multiple output sets of the output storage values are preprocessed by circuitry (48) that is fabricated on the first semiconductor die, to produce preprocessed data. The preprocessed data is provided to a memory controller (28), which is fabricated on a second semiconductor die that is different from the first semiconductor die, so as to enable the memory controller to reconstruct the data responsively to the preprocessed data.