The equations of multiple-scattering theory (MST) are solved for the case of a lattice of square-well potentials in the shape of squares that fill the plane. We find that multiple-scattering theory is exact within reasonably achievable numerical accuracy. There is a problem with the convergence of MST in its traditional formulation that has obscured the fact that it is an exact theory even for non-muffin-tin, space-filling potentials. We show that this problem can be easily circumvented and describe a rapidly convergent, exact formulation of MST. © 1990 The American Physical Society.