A nonvolatile memory with a multi-pass programming scheme enables a page of multi-level memory cells to be programmed with reduced floating-gate to floating-gate perturbations (Yuping effect). The memory cells operate within a common threshold voltage range or window, which is partitioned into multiple bands to denote a series of increasingly programmed states. The series is divided into two halves, a lower set and a higher set. The memory cells are programmed in a first, coarse programming pass such that the memory cells of the page with target states from the higher set are programmed to a staging area near midway in the threshold window. In particular, they are programmed closer to their targeted destinations than previous schemes, without incurring much performance penalty. Subsequent passes will then complete the programming more quickly. Yuping effect is reduced since the threshold voltage change in subsequent passes are reduced.