Using nuclear double resonance with spin mixing by level crossing (DRLC) the nuclear quadrupole resonance spectrum for 2D and 7O have been obtained at 77 K in isotopically enriched Ice II, a proton-ordered high-pressure phase of ice. Four inequivalent deuterium sites were found which could be assigned in pairs to two inequivalent water molecules with the aid of a double quadrupole resonance spectrum. The electric field gradient parameters for the deuterium sites of one molecule are e2gQ/h = 225.8 ± 0.3 kHz; η = 0.127 ± 0.005 and e2gQ/h = 219.8 ± 0.3 kHz, η = 0.134 ± 0.005; and for the other are e2gQ/h = 226.1 ± 0.3 kHz, η = 0.100 ± 0.005 and e2qQ/h = 220.3 ± 0.3 kHz, η = 0.102 ± 0.005. For the 17O site in fully protonated Ice II, e2qQ/h = 6983 ± l0kHz, η = 0.865 ± 0.007. The implications of these results in elucidating the structure of Ice II are discussed.