Non-volatile storage elements are programmed in a manner that reduces program disturb by using modified pass voltages. In particular, during the programming of a selected storage element associated with a selected word line, a higher pass voltage is applied to word lines associated with previously programmed non-volatile storage elements in the set than to word lines associated with unprogrammed and/or partly programmed non-volatile storage elements in the set. The pass voltage is sufficiently high to balance the channel potentials on the source and drain sides of the selected word line and/or to reduce leakage of charge between the boosted channel regions. Optionally, an isolation region is formed between the boosted channel regions by applying a reduced voltage on one or more word lines between the selected word line and the word lines that receive the higher pass voltage.