Rheological parameters for ice II and ice III, needed in tectonic models of the icy satellites of the major planets, are obtained from extrusion experiments and compared with the rheology of ice I at pressures ~2 kbar and temperatures ~240k. Ice II has a higher effective viscosity (by a factor ~10) than ice I at similar stress levels, whereas ice III has a lower viscosity (by a factor ~0.01). The rheological contrasts among the ice phases are related to differences in the dielectric relaxation behavior and state of proton order/disorder in the structures in a way that sheds light on the nature of dislocation motion in ice. A striking transformation plasticity accompanies the ice I--III transition and could have large tectonic effects.