Large single crystals of ice III, ice V, and ice VI have been grown and in situ Brillouin spectra collected at various crystal orientations, The elastic constants have been calculated at -20 degrees C and 2.2 kbar, -35 degrees C and 3.0 kbar, and -2 degrees C and 7.2 kbar for ice III, ice V, and ice VI, respectively. The data were used to calculate the isotropic elastic constants of polycrystalline aggregates of each phase, and the results are compared with known polycrystalline data.