A "smart verify" technique, whereby multi-state memories are programmed using a verify-results-based dynamic adjustment of the multi-states verify range for sequential-state-based verify implementations, is presented. This technique can increase multi-state write speed while maintaining reliable operation within sequentially verified, multi-state memory implementations by providing "intelligent" means to minimize the number of sequential verify operations for each program/verify/lockout step of the write sequence. At the beginning of a program/verify cycle sequence only the lowest state or states are checked during the verify phase. As lower states are reached, additional higher states are added to the verify sequence and lower states can be removed.