A method for data storage includes storing data in a group of memory cells, by encoding the data using at least an outer code and an inner code, and optionally inverting the encoded data prior to storing the encoded data in the memory cells. The encoded data is read from the memory cells, and inner code decoding is applied to the read encoded data to produce a decoding result. At least part of the read data is conditionally inverted, depending on the decoding result of the inner code.