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. Non-volatile storage elements being programmed to a first set of one or more targets are verified to determine whether they have reached their target and are locked out of further programming if it is determined that they have reached their target. Non-volatile storage elements being programmed to the second set of one or more targets are tested to determine the number of fast programming bits. When the number of fast bits for a particular target is greater than a threshold, then programming stops for the non-volatile storage elements being programmed to the particular target.