The unintentional programming of an unselected (or inhibited) non-volatile storage element during a program operation that intends to program another non-volatile storage element is referred to as “program disturb.” A system is proposed for programming and/or reading non-volatile storage that reduces the effect of program disturb. In one embodiment, different verify levels are used for a particular word line (or other grouping of storage elements) during a programming process. In another embodiment, different compare levels are used for a particular word (or other grouping of storage elements) during a read process.