Charge scaling has proven to be an efficient way to account in a mean-field way for electronic polarization by
aqueous ions in force field molecular dynamics simulations. However, commonly used water models with dielectric
constants over 50 are not consistent with this approach leading to ’overscaling’, i.e., generally too weak ion-ion
interactions. Here, we build water models fully compatible with charge scaling, i.e., having the correct low-frequency
dielectric constant of about 45. To this end, we employ advanced optimization and machine learning schemes in
order to explore the vast parameter space of 4-site water models efficiently. As an a priori unwarranted positive result,
we find a sizable range of force field parameters that satisfy the above dielectric constant constraint providing at the
same time accuracy with respect to experimental data comparable with the best existing 4-site water models such
as TIP4P/2005, TIP4P-FB, or OPC4. The present results thus open the way to the development of a consistent
charge scaling force field for modelling ions in aqueous solutions.