A group of non-volatile memory cells are programmed in a programming pass by a series of incremental programming pulses where each pulse is followed by a program-verify and possibly program-inhibition step. Performance is improved during the programming pass by delayed starting and prematurely terminating the various verify levels that demarcate the multiple memory states. This amounts to skipping the verifying and inhibiting steps of the fastest and slowest programming (fringe) cells of the group. A reference pulse is established when the fastest cells have all been program-verified relative to a first verify level. The starting of what verify level at what pulse will then be delayed relative to the reference pulse. Verifying stops for a given verify level when only a predetermined number of cells remain unverified relative to that given level. Any errors arising from over- or under-programming of the fringe cells are corrected by an error correction code.