The quality of data stored in a memory system is assessed by different methods, and the memory system is operated according to the assessed quality. The data quality can be assessed during read operations. Subsequent use of an Error Correction Code can utilize the quality indications to detect and reconstruct the data with improved effectiveness. Alternatively, a statistics of data quality can be constructed and digital data values can be associated in a modified manner to prevent data corruption. In both cases the corrective actions can be implemented specifically on the poor quality data, according to suitably chosen schedules, and with improved effectiveness because of the knowledge provided by the qualify indications. These methods can be especially useful in high-density memory systems constructed of multi-level storage memory cells.