The low-energy scattering by a potential consisting of a long- and a short-range part is discussed. A general expression for the phase shift δL is derived starting from the radial Schrödinger equation. Effective-range expansions are presented for partial waves of all orders for the case of a long-range r-8 potential. The quantity δL is calculated up to and including the term k2L+7lnk. It is found that in the low-energy limit, δL is proportional to k2L+1 for s, p, and d waves, and δL is proportional to k6 for all the higher partial waves.