A method for data storage includes accepting data for storage in a memory (28) that includes multiple analog memory cells (32). The data is converted to input values. The input values are filtered using a non-linear filtering operation to produce respective shaped values, and the shaped values are converted to output values using a linear spreading transformation with coefficients chosen so that each of the shaped values contributes to at least two of the output values. The non-linear filtering operation is selected so as to reduce a size of an output range in which the output values lie. The output values are stored in the respective analog memory cells.