Using a form of three-body perturbation theory we have calculated directly the energy shift for the Kα transition (2p-1s) in the π-d system without evaluating the pion-deuteron scattering length by the usual multiple scattering formalism. We have critically investigated the essential limitations of the formula of Deser et al. relating the zero-energy scattering amplitude to the energy shift. We find that the contribution to the lowest order shift due to the off-shell energy dependence of the pion-nucleon t-matrix is appreciable. To confirm the importance of the off-shell correction to the single scattering term, the significance of multiple-scattering processes in the perturbation expansion is considered. The contribution of all rescatterings of the pion on the nucleons, which constitutes the total first-order shift is evaluated. A bound on the magnitude of the second-order shift, which allows nucleon-nucleon rescattering, is also given.