Different approaches to improve the simple point charge model for liquid water (SPC) were investigated. This led to a whole series of new water models with additional van der Waals interaction sites at the hydrogen atoms, modified partial charges and modified geometries. The properties of these models are analyzed and discussed. Particular emphasis has been put on the study of the dependence and sensitivity of water properties on the model parameters. We found that a simultaneous improvement of the dielectric permittivity and the diffusion coefficient is difficult to attain for a rigid, nonpolarizable three interaction site model. Nevertheless, two of the models presented here, SPC/A and SPC/L, show good agreement with experimental data on water and have been characterized in more detail. We conclude that SPC/L represents the overall properties of water better than SPC. Especially, it shows excellent dielectric properties, an improved shear viscosity and a slightly lower diffusion coefficient.