The influence of rotational state on the dissociation probability of H-2 on Cu(111) has been investigated with 3- and 4-dimensional close-coupling wave packet calculations. Recent experimental results have shown that the energetic threshold for dissociative adsorption increases and then decreases as the J state is continuously increased. This trend can be faithfully reproduced by modeling the H-2 as a planar (cartwheel) rotor scattering from a flat surface. The agreement disappears when the model is extended to a 3-dimensional rotor. Further, the degenerate m(J) states have a spread of dissociation probabilities which results in a broad smearing of the dissociation threshold. This effect, which is absent from experiment, increases with J(i). These shortcomings can be partially corrected by corrugating the potential in the azimuthal coordinate in accord with recent ab initio results. The dynamical calculations also exhibit strong rotational inelasticity for the scattered fraction, during dissociation. Since this system has a late barrier for dissociation, we show that the rotational inelasticity should be enhanced by initial vibrational state. Our 4-dimensional modeling is unable simultaneously to match the relative positions of dissociation and vibrational excitation thresholds. We speculate that these processes occur on different surface sites.