A method for programming a non-volatile memory system. The method includes programming a first non-volatile storage element on a first word line and a first NAND string to store "n" bits of data. A second non-volatile storage element on the first word line and a second NAND string is programmed to store n+1 bits of data. The second non-volatile storage element is a neighbor to the first non-volatile storage element. A third non-volatile storage element on a second word line and the second NAND string is programmed to store n bits of data. The third non-volatile storage element is a neighbor to the second non-volatile storage element. A fourth non-volatile storage element on the second word line and the first NAND string is programmed to store n+1 bits of data.