The authors consider classical elastic scattering by a potential with a P2 anisotropic component and find that the isotropic rainbow is replaced by cusps in the cross section reflecting features of the potential surface. Using perturbation theory, analytic expressions for these points are found for a LJ(2n, n) potential. The predictions are in qualitative agreement with observations on Li+-N2, CO. In-plane approximations are considered and found to be satisfactory for physically realistic potentials. The authors also examine body-fixed-type approximations and find that these can be significantly in error in the rainbow region.