In this work the 4-point polarizable SWM4 Drude water model is reparametrized. Multiple models were developed using different strategies toward reproduction of specific target data. Results indicate that no individual model can reproduce all the selected target data in the context of the present form of the potential energy function. The changes considered in the new models include, 1) variations in the gas phase dipole moment, 2) variations in the molecular polarizability, 3) variations of the distance between the oxygen and the M site, 4) variation of the oxygen Lennard-Jones (LJ) parameters, 5) introduction of a LJ potential to the hydrogen atoms, and 6) variations of the H-O-H angle. Detailed analysis is presented for 3 new water models from which a final model, SWM4-HLJ, is selected as the future default model for the Drude polarizable force field. The model maintains the gas phase dipole moment as the experimental value while the remaining listed terms were adjusted including a larger H-O-H angle (108.12). Compared to its predecessor, SWM4-NDP, the self-diffusion coefficient, water dimer properties, and water cluster energies are greatly improved. The temperature dependence of the density of the new model also performs better. Overall, the new SWM4-HLJ water model is a general improvement and a good balance between microscopic and bulk properties is achieved.