An erase operation for a 3D stacked memory device applies an erase pulse which includes an intermediate level (Vgidl) and a peak level (Verase) to a set of memory cells, and steps up Vgidl in erase iterations of the erase operation. Vgidl can be stepped up when a specified portion of the cells have reached the erase verify level. In this case, a majority of the cells may have reached the erase verify level, such that the remaining cells can benefit from a higher gate-induced drain leakage (GIDL) current to reached the erase verify level. Verase can step up before and, optionally, after Vigdl is stepped up, but remain fixed while Vgidl is stepped. Vgidl can be stepped up until a maximum allowed level, Vgidl_max, is reached. Vgidl may be applied to a drain-side and/or source-side of a NAND string via a bit line or source line, respectively.