On compressing low-density amorphous ice (LDA) at 125 K up to 1.6 GPa, two distinct density steps accompanied by heat evolution are observable in pressure-density curves. Samples recovered to 77 K and 1 bar after the first and second steps show the x-ray diffraction pattern of high-density amorphous ice (HDA) and very HDA (VHDA), respectively. The compression of the once formed HDA takes place linearly in density up to 0.95 GPa, where nonlinear densification and HDA -> VHDA conversion is initiated. This implies a stepwise formation process LDA -> HDA -> VHDA at 125 K, which is to the best of our knowledge the first observation of a stepwise amorphous-amorphous-amorphous transformation sequence. We infer that the relation of HDA and VHDA is very similar to the relation between LDA and HDA except for a higher activation barrier between the former. We discuss the two options of thermodynamic versus kinetic origin of the phenomenon
