Brillouin spectroscopy has been used to determine the adiabatic elastic constants of Ice III at -20 degrees C and 2.2 kbar. A new technique was used to grow large single crystals. The adiabatic moduli were found to be C-11=153.7, C-12=99.5, C-13=65.1, C-33=115.5, C-44=44.6, C-66=56.8 kbar. An averaging method was used in conjunction with these constants to determine longitudinal and transverse velocities and elastic moduli for isotropic polycrystalline aggregates and compared to previous values. This work is now being extended to ice II, IV, V, and VI.