In each row of a nonvolatile memory array, the select gates of all the memory cells are connected together and are used to select a row for memory access. The control gates of each row are also connected together, and the source regions of each row are connected together. Also, the control gates of plural rows are connected together, and the source regions of plural rows are connected together, but if the source regions of two rows are connected together, then their control gates are not connected together. If one of the two rows is being accessed but the other one of the two rows is not being accessed, their control gates are driven to different voltages, reducing the probability of a punch-through in the non-accessed row.