An erase process for a 3D stacked memory device performs a two-sided erase of NAND strings until one of more of the NAND strings passes an erase-verify test, then a one-sided erase of the remaining NAND strings is performed. The two-sided erase charges up the body of a NAND string from the source-side and drain-side ends, while the one-sided erase charges up the body of the NAND string from the drain-side end. The NAND strings associated with one bit line form a set. The switch to the one-sided erase can occur when the set meets a set erase-verify condition, such as one, all, or some specified portion of the NAND strings of the set passing the erase-verify test. The erase operation can end when no more than a specified number of NAND strings have not met the erase-verify test. As a result, erase degradation of the memory cells is reduced.