In this article, we describe how the fitting of surface tension is enabled by extending the ForceBalance optimization method to include surface tension as a fitting target. To demonstrate feasibility, we develop and characterize two new water models, namely TIP3P-ST and TIP4P-ST (here ST stands for "surface tension"), where the surface tension property replaces the heat of vaporization in the training data. The resulting TIP4P-ST model confirms our hypothesis by exhibiting high accuracy for thermodynamic properties across a range of temperatures, for both training and validation data that include the density, dielectric constant, isothermal compressibility, thermal expansion coefficient, and self-diffusion coefficient. The TIP3P-ST model offers moderate agreement with the full range of data, but reproduces the correct temperature of maximum density of water for the first time in models of this form.