We report a direct measurement of the molecular axis orientation dependence of dissociative neutralisation of 2.98 keV H-2+ at a Cu(111) surface. The kinetic energy epsilon-released and the final orientation theta of the molecular axis to the surface normal are derived from the measured laboratory-frame velocities of the neutral dissociation fragments. Above an incident beam perpendicular energy E perpendicular-to i almost-equal-to 3.5 eV the epsilon-energy distribution appears to consist of one structure peaking at or below epsilon almost-equal-to 0.75 eV. As we reduce E perpendicular-to i, an additional broad structure peaking at epsilon almost-equal-to 3 eV, theta almost-equal-to 60-degrees appears. The intensity ratio of these two structures remains approximately constant for E perpendicular-to i values below 1 eV. We propose that neutralisation occurs on the incident portion of the trajectory, primarily to the (surface modified) X1-SIGMA(g+) state of H-2, and furthermore, that the observed change of the spectrum with E perpendicular-to i may be related to reflection from (for E perpendicular-to i < 1 eV) and traversal over (for E perpendicular-to i > 1 eV) an activation barrier of height approximately 1 eV on the H-2/Cu potential energy surface.