Various embodiments of the invention pertain to a technique of recovering data from a portion of a non-volatile memory which was not reliably read because the number of read errors exceeded the ability of the ECC process to correct those errors. For each cell in that portion of memory, a quantized estimate is made of the amount of offset in the read reference voltage that is predicted to correct for any systematic noise that may have affected the reading of that cell. For each quantized offset, the read reference voltage is adjusted by that amount and data from the relevant cells is read. The combined results for all the cells are then processed through the ECC again.