Most of the experimental information on high-energy scattering from neutrons has been obtained by comparing cross-sections from protons and deuterons. The extraction of neutron cross-sections from such data is nontrivial; the most widely used model is the semiclassical ray formula of Glauber, which gives, in addition to the impulse approximation terms, a shadow correction due to the mutual «eclipsing» of the nucleons in the deuteron. In this paper we show that, if the nucleon-nucleon scattering amplitudes near the forward direction can be represented as a sum of Regge poles, the shadow term that Glauber includes vanishes rapidly at high energies but that other terms remain which provide a somewhat smaller shadow effect. We first give a diagrammatic derivation of the Glauber formula and show that his shadow term, which comes from the diagram where both nucleons interact with the incident fast particle, does not in fact have the Regge cut necessary for its persistence at high energies. We then show that certain diagrams with inelastic virtual states between the two interactions do have such cuts and we express their contribution in terms of a partial inelastic crosssection and a statistical factor. An experimental clarification can only be achieved by accurate experiments with high-energy neutron beams.