Capacitive coupling from storage elements on adjacent bit lines is compensated by adjusting voltages applied to the adjacent bit lines. An initial rough read is performed to ascertain the data states of the bit line-adjacent storage elements, and during a subsequent fine read, bit line voltages are set based on the ascertained states and the current control gate read voltage which is applied to a selected word line. When the current control gate read voltage corresponds to a lower data state than the ascertained state of an adjacent storage element, a compensating bit line voltage is used. Compensation of coupling from a storage element on an adjacent word line can also be provided by applying different read pass voltages to the adjacent word line, and obtaining read data using a particular read pass voltage which is identified based on a data state of the word line-adjacent storage element.