Disturbs are reduced during programming and read operations for drain-side memory cells in a string by controlling dummy word line portions separately in selected and unselected sub-blocks. One or more of the dummy word line layers are separated so that they can be driven with different voltages. This allows the channel gradient to be optimized to reduce the likelihood of disturbs. In another aspect, a stack of alternating conductive and dielectric layers is formed in two parts, with lower pillars which comprise select gate transistors, source-side dummy memory cells and data memory cells, below upper pillars which comprise drain-side dummy memory cells and select gate transistors. The upper pillars are relatively narrow to provide a more compact structure. Moreover, the centerline of some upper pillars can be offset from the centerline of corresponding lower pillars to provide room for an isolation region.