The development of accurate molecular mechanics force fields is a significant challenge that must be addressed for the continued success of molecular simulation. We apply the recently developed ForceBalance method to automatically derive accurate force field parameters using flexible combinations of experimental and theoretical reference data. The method is demonstrated in the parametrization of two rigid water models with an alternative functional form describing van der Waals nonbonded interactions, yielding new parameter sets (TIP3P-FBV and TIP4P-FBV) that accurately describe many physical properties of water.