A recently proposed method for calculating the bound rotational-vibrational energy levels of triatomic molecules is applied to the Ar—HCl van der Waals complex and to the water molecule. For Ar—HCl energy levels, rotational constants and centrifugal distortion constants for several different potential-energy functions are calculated. The accuracy of the calculations is critically examined and is found to be very high. It is demonstrated that the method may be used to calculate the higher lying rotational–vibrational energy levels of the complex without either a significant loss of accuracy or any large increase in computational effort. The complete set of rotational–vibrational energy levels is calculated for two different Ar—HCl potentials and for several different values of the total angular momentum. The coupled states or p-helicity decoupling approximation, which has been used previously in the context of molecular scattering theory, is examined and shown to yield very reliable results. This approximation greatly reduces the computational effort required to perform calculations, especially for higher values of the total angular momentum. In the case of the water molecule we examine the use of a “hindered-rotor” basis set, and show that we are able to obtain a faster rate of convergence and greater accuracy for the low-lying energy levels of water with this type of basis.