We have studied copper corrosion in a system comprised of deionized water, absolute pressure gauges, and a palladium membrane. A transition from O-2-consuming to H-2-evolving copper corrosion is observed, which indicates that copper can corrode by water itself. The equilibrium hydrogen pressure in corrosion of copper by water at 73 degrees C exceeds the steady-state atmospheric hydrogen pressure (5 x 10(-7) bar) by a factor of about 2000. The growth of a hydrogen-containing corrosion product in O-2-free water is controlled by the hydrogen removal from the corroding surface. The results are discussed in the perspective of conventional potential-pH diagram for copper.