A method for data readout includes storing two or more candidate sets of read thresholds for reading from a memory device that includes a plurality of analog memory cells. A group of the memory cells from which data is to be read is identified. An order is defined among the candidate sets of the read thresholds responsively to a criterion defined over the group of the memory cells. Data readout from the group of the memory cells is attempted by iterating over the candidate sets according to the order, until the data is read successfully.