Near-resonant vibrational energy exchange between oxygen and water molecules is an important process in the Earth's atmosphere, combustion chemistry, and the chemical oxygen iodine laser ( COIL). The reactions in question are (1) O-2(1) + O-2(0) -> O-2(0) + O-2(0); (2) O-2(1) + H2O(000) -> O-2(0) + H2O(000); (3) O-2(1) + H2O(000) <-> O-2(0) + H2O(010); (4) H2O(010) + H2O(000) -> H2O(000) + H2O( 000); and ( 5) H2O( 010) + O-2(0) -> H2O(000) -> O-2(0). Reanalysis of the data available in the chemical kinetics literature provides reliable values for rate coefficients for reactions 1 and 4 and strong evidence that reactions 2 and 5 are slow in comparison with reaction 3. Analytical solution of the chemical rate equations shows that previous attempts to measure the rate of reaction 3 are unreliable unless the water mole fraction is higher than 1%. Reanalysis of data from the only experiment satisfying this constraint provides a rate coefficient of (5.5 +/- 0.4) x 10(-13) cm(3)/s at room temperature, between the values favored by the atmospheric and laser modeling communities.