High resolution inelastic neutron scattering spectra of CH4, CH4/CD4 mixtures, and CH3D adsorbed on exfoliated graphite at 4.5 K have been obtained. The resolution used was approximately five times higher than previously used and has revealed extra detail in the spectra. For CH4 it is shown that the parameter, H, related to rotation about the twofold axes is not exactly zero. It has an unexpected small positive value. For a 1:2 CH4/CD4 mixture the tunneling spectra of the CH4 show that the mixture must be ordered at 4.5 K and that the barriers to rotation of the CH4 are increased slightly when the surrounding CH4 molecules are replaced by the heavier CD4. For CH3D the higher resolution spectra make it possible to make an unambiguous assignment of the tunneling spectra, which is different from that previously proposed. The assignment indicates that there are terms in the orientational potential higher than the threefold Fourier components previously assumed, but that these probably do not affect the derived heights of the barriers to rotation of methane on graphite.