An erase operation for a 3D stacked memory device selectively inhibits subsets of memory cells which meet a verify condition as the erase operation progresses. As a result, the faster-erasing memory cells are less likely to be over-erased and degradation is reduced. Each subset of memory cells can be independently erased by controlling a select gate, drain (SGD) transistor line, a bit line or a word line, according to the type of subset. For a SGD line subset or a bit line subset, the SGD line or bit line, respectively, is set at a level which inhibits erase. For a word line subset, the word line voltage is floated to inhibit erase. An inhibit or uninhibit status can be maintained for each subset, and each type of subset can have a different maximum allowable number of fail bits.