In our recent studies, evidence was presented that a relaxed ice nanocrystal surface is disordered, in contrast to the nanocrystal interior. In this study it is argued, based on spectroscopic evidence, that disorder extends to several surface layers. Difference spectra between large and small D2O nanocrystals are used to obtain the infrared OD stretch absorption of the disordered subsurface layers. Moreover it is shown that certain select adsorbates at the ice surface induce a significant ordering of the ice subsurface as indicated by the conversion of one-third or more of the subsurface spectrum to that of interior ice. For ice nanocrystals, the new “interior” ice can be greater than 10% of the total amount of ice. Since the ice subsurface apparently consists of approximately three bilayers, this suggests that the influence of these adsorbates on the surface bilayer is reflected in the “ordering” of one or more subsurface bilayers. Examples of adsorbates that have this influence are the bifunctional molecules acetylene and H2S, either of which can act effectively as both proton donor and proton acceptor, while more weakly bonded small molecule adsorbates, such as N2 and CO, do not noticeably influence the subsurface structure. It is suggested that, by engaging in significant H-bonding with the unsaturated surface groups of the top bilayer (dangling-H and dangling-O molecules), the bifunctional adsorbates reverse the restructuring of the outer layer of ice that occurs with an increase of the number of H-bonds of the surface water molecules. This, in turn, reduces the distortion of the ice surface and the displacement of molecules within the ice subsurface layers that accompanies the restructuring. The new data and interpretation give strong support to the view that the equilibrium ice surface has a high degree of structural disorder.