The dependence of single-crystal Brillouin spectra on both crystal orientation and pressure (P) has been measured for phases III and VI of ice. The conditions, with P in kbar, were T = -20 degrees C, 2.2 less than or equal to P less than or equal to 3.0 for ice III, and T = -2 degrees C, 6.2 less than or equal to P less than or equal to 8.2 for ice VI. The pressure dependencies of the elastic constants and the polycrystalline elastic properties were determined. (C) 1997 American Institute of Physics.