Velocities of NO molecules scattered from Ag(111) have been measured as a function of rotational state for a wide range of incidence energies and angles. We find that increasing rotational excitation is accompanied by decreasing energy transfer to phonons. Results agree quantitatively with an extensive trajectory simulation employing a realistic multidimensional interaction potential, which shows that this correlation is mediated largely by the orientation angle of the colliding molecule. A simple kinematic model suggests that this behavior is a general feature of molecule-surface scattering. © 1986 The American Physical Society.