Abstract. The vector spherical-multipole analysis is applied to determine the scattering of a plane electromagnetic wave by a perfectly electrically conducting (PEC) semi-infinite elliptic cone. From the eigenfunction expansion of the total field in the space outside the elliptic cone, the scattered far field is obtained as a multipole expansion of the free-space type by a single integration over the induced surface currents. As for the evaluation of the free-space-type expansion it is necessary to apply suitable series transformation techniques, a sufficient number of eigenfunctions has to be considered. The eigenvalues of the underlying two-parametric eigenvalue problem with two coupled Lamé equations belong to the Dirichlet- or the Neumann condition and can be arranged as so-called eigenvalue curves. It has been observed that the eigenvalues are in two different domains: In the first one Dirichlet- and Neumann eigenvalues are either nearly coinciding, while in the second one they are strictly separated. The eigenfunctions of the first (coinciding) type look very similar to free-space modes and do not contribute to the scattered field. This observation allows to significantly improve the determination of diffraction coefficients.