We report the iAMOEBA (“inexpensive AMOEBA”) classical polarizable water model. The iAMOEBA model uses a direct approximation to describe electronic polarizability, in which the induced dipoles are determined directly from the permanent multipole electric fields and do not interact with one another. The direct approximation reduces the computational cost relative to a fully self-consistent 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 efficiently utilizing the available data.