We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.