Based on extensive studies of existing potentials we propose a new molecular model for water. The new model is rigid and contains three Gaussian charges. Contrary to other models, all charges take part in the polarization of the molecule. They are connected by harmonic springs to their gas-phase positions: the negative charge to a prescribed point on the main axis of the molecule; the positive charges to the hydrogens. The mechanical equilibrium between the electrostatic forces and the spring forces determines the polarization of the molecule which is established by iteration at every timestep. The model gives excellent estimates for ambient liquid properties and reasonably good results from high-pressure solids to gas-phase clusters. We present a detailed description of the development of this model and a large number of calculated properties compared to the estimates of the nonpolarizable TIP4P/2005 [J. L. F. Abascal and C. Vega, J. Chem. Phys. 123, 234505 (2005)10.1063/1.2121687], the polarizable GCPM [P. Paricaud, M. Predota, A. A. Chialvo, and P. T. Cummings, J. Chem. Phys. 122, 244511 (2005)10.1063/1.1940033], and our earlier BKd3 model [P. T. Kiss and A. Baranyai, J. Chem. Phys. 137, 084506 (2012)10.1063/1.4746419]. The best overall performance is shown by the new model.