The high-pressure form of solid water, ice III, is the equilibrium phase in contact with liquid water at pressures from about 2.0 - 3.5 kbar. Consequently, its properties are important in calculating the volume changes on freezing of subsurface oceans inside icy planetary bodies and the buoyancy of icy volcanic melts. The incompressibility (bulk modulus) of ice III as found by quantum mechanical simulations is much lower (<60%) than that of the ice phases at neighbouring pressures and temperatures, but the very small stability field of ice III makes its experimental determination difficult. We have a few measurements within its stability field from a recent OSIRIS experiment, and we now intend to combine these with measurements on metastable ice III (= ice IX, when proton ordered) to much higher pressures on PEARL to obtain both the incompressibility and its temperature dependence.