The three-component clathrate H-2-TDF-D2O Offers hydrogen storage at lower pressure, but with reduced weight fraction of H-2, compared to H-2-H2O clathrate. In H-2-TDF-D2O, H2 resides exclusively and singly in the small cages of structure II, allowing the rotational behavior of H-2 in this nominally uniform environment to be probed. Here we report NMR measurements of the H-2 line shape and relaxation times T-1, T-2, and T-1p. The principal differences in the results, compared to the H-2-D2O binary system, are the dips in T-2 and T-1p near 28 K due to thermally activated reorientation of TDF molecules, line-narrowing and decreases in T2 and T-1p near 175 K due to D2O reorientations and diffusion, and the apparent absence of H-2 diffusion between small cages.