Higher-lying five-dimensional translation-rotation (T-R) eigenstates of a single p-H-2 and o-D-2 molecule confined inside the small dodecahedral (5 12) Cage of the structure 11 clathrate hydrate are calculated rigorously, as fully coupled, with the cage assumed to be rigid. The calculations cover the excitation energies up to and beyond the j = 2 rotational level of the free molecule, 356 cm(-1) for H-2 and 179 cm(-1) for D-2. It is found that j is a good quantum number for all the T-R states of p-H-2, j = 0 and j = 2, considered. The same is not true for o-D-2, where a number of T-R states in the neighborhood of the j = 2 level show significant mixing of j = 0 and j = 2 rotational basis functions. The 5-fold degeneracy of the j = 2 level of p-H-2 is lifted completely due to the anisotropy of the cage environment, as is the 3-fold degeneracy of the j = 1 level of o-H-2 studied by us previously. Pure translational mode excitations with up to four quanta display negative anharmonicity, which was observed earlier for the translational fundamentals and their first overtones. The issues of assigning the combination states of p-H-2 with excitations of two or all three translational modes, and of the strength of the mode coupling as a function of the excitation energy, are studied carefully for a range of quantum numbers. The average T-R energy of the encapsulated p-H-2 is calculated as a function of temperature from 0 to 150 K.