Errors can occur when reading the threshold voltage of a programmed non-volatile storage element due to at least two mechanisms: (1) capacitive coupling between neighboring floating gates and (2) changing conductivity of the channel area after programming (referred to as back pattern effect). To account for coupling between neighboring floating gates, the read process for a particular memory cell will provide compensation to an adjacent memory cell in order to reduce the coupling effect that the adjacent memory cell has on the particular memory cell. To account for the back pattern effect, a first voltage is used during a verify operation for unselected word lines that have been subjected to a programming operation and a second voltage is used for unselected word lines that have not been subjected to a programming operation. The combination of these two techniques provides for more accurate storage and retrieval of data.