We report the iAMOEBA (i.e. “inexpensive AMOEBA”) classical polarizable water model. iAMOEBA uses a direct approximation to describe electronic polarizability, which reduces the computational cost relative to a fully polarizable model such as AMOEBA. The model is parameterized using ForceBalance, a systematic optimization method that simultaneously utilizes training data from experimental measurements and high-level ab initio calculations. We show that iAMOEBA is a highly accurate model for water in the solid, liquid, and gas phases, with the ability to fully capture the effects of electronic polarization and predict a comprehensive set of water properties beyond the training data set including the phase diagram. The increased accuracy of iAMOEBA over the fully polarizable AMOEBA model demonstrates ForceBalance as a method that allows the researcher to systematically improve empirical models by optimally utilizing the available data.