Coupling effects between adjacent floating gates in a non-volatile storage device are reduced in a multi-pass programming operation, while reducing program data storage requirements. In one approach, storage elements are programmed in an out of sequence or zigzag word line order. A particular word line is programmed with a coarse program pass, after which another word line is programmed with a fine program pass, after which the particular word line is read. The particular word line is read before another word line is programmed with a coarse program pass which causes coupling interference to storage elements of the particular word line. The read data is subsequently used to perform a fine program pass for the particular word line. This avoids the need to store program data of multiple word lines concurrently, so that storage hardware can be reduced in size along with power consumption.