The results we obtain are significant for two main reasons. Firstly, we demonstrate that by selecting optimization targets spanning different scales (micro + macro), such as the RDFs, density, and dielectric constant, it is possible to obtain an optimized water model with comparable accuracy to state-of-the-art models like TIP3P-FB and OPC3, while maintaining computational efficiency and robustness. Secondly, our findings allow us to investigate the chemical and physical origins that control the accuracy limits (indeterminacy) of model optimization. We investigate how these limits are intrinsic and connected to the physical constraints of the model itself. The insights gained from this study hold significance not only for optimizing the specific system presented in this paper but also for any approxi-mated model that relies on higher-accuracy data or incorporates top-down constraints based on experimental evidence.