A set of non-volatile storage elements are subjected to a programming process in order to store data. During the programming process, one or more verification operations are performed to determine whether the non-volatile storage elements have reached their target condition to store the appropriate data. Programming can be stopped when all non-volatile storage elements have reached their target level or when the number of non-volatile storage elements that have not reached their target level is less than a number or memory cells that can be corrected using an error correction process during a read operation (or other operation). The number of non-volatile storage elements that have not reached their target level can be estimated by counting the number of non-volatile storage elements that have not reached a condition that is different (e.g., lower) than the target level.