Nearly exact six-dimensional quantum calculations of the vibration-rotation-tunneling (VRT) levels of the water dimer for values of the rotational quantum numbers J and K less than or equal to2 show that the SAPT-5s water pair potential presented in the preceding paper (paper I) gives a good representation of the experimental high-resolution far-infrared spectrum of the water dimer. After analyzing the sensitivity of the transition frequencies with respect to the linear parameters in the potential we could further improve this potential by using only one of the experimentally determined tunneling splittings of the ground state in (H2O)(2). The accuracy of the resulting water pair potential, SAPT-5st, is established by comparison with the spectroscopic data of both (H2O)(2) and (D2O)(2): ground and excited state tunneling splittings and rotational constants, as well as the frequencies of the intermolecular vibrations.