The electrophoretic motion of a charged sphere in the presence of a rigid boundary is analyzed for low surface zeta potentials but arbitrary kappa a, where a is the particle radius and kappa is the inverse Debye length. The boundary configurations considered are a single flat wall, a slit, and a long cylindrical tube. Using a method of reflections, we obtain the particle velocity for a constant applied electric held in powers of lambda up to O(lambda(6)), where lambda is the ratio of the particle radius to the distance from the boundary. This analysis is valid as long as the double layer around the particle does not overlap significantly with the double layer at the boundary. The effect of finite kappa a is to enhance the viscous retardation of the particle, although for large separations the first effect due to the proximity of the boundary is still at O(lambda(3)) in all cases. When the applied held is parallel to the boundary, the electrophoretic velocity is not proportional to the difference in zeta potential between the particle and the boundary (as occurs for kappa a --> infinity), and the proximity of the boundary may increase the particle velocity or change its direction. An important result of the analysis is that the hindrance to the electrophoretic velocity of a particle in a cylindrical pore increases significantly as kappa a is reduced below 10.