Water is a notoriously difficult substance to model both accurately and efficiently. Here, we focus on descriptions with a single coarse-grained particle per molecule using the so-called approximate non-conformal and generalized Stockmayer potentials as the starting points. They are fitted using the radial distribution function and the liquid-gas density profile of the atomistic extended simple point charge (SPC/E) model by downhill simplex optimization. We compare the results with monatomic water (mW), ELBA, and direct iterative Boltzmann inversion of SPC/E. The results show that symmetrical potentials result in non-transferable models, that is, they need to be reparametrized for new state points. This indicates that transferability may require more complex models. Furthermore, the results also show that the addition of a point dipole is not sufficient to make the potentials accurate and transferable to different temperatures (300 K-500 K) and pressures without an appropriate choice of properties as targets during model optimization.