A three dimensional non-volatile storage system includes a substrate and a plurality of memory cells arranged in a monolithic three dimensional memory array (or other 3D structure) positioned above and not in the substrate. The system includes a plurality of vertical bit lines and a plurality of word lines. Each group of three neighboring word lines on a common level of the three dimensional memory array are electrically isolated from each other and at least a subset of the three neighboring word lines of each group are connected to other word lines.