As optical frequency nanoantennas, reduced-symmetry plasmonic nanoparticles have light-scattering properties that depend strongly on geometry, orientation, and variations in dielectric environment. Here we investigate how these factors influence the spectral and angular dependence of light scattered by Au nanocups. A simple dielectric substrate causes the axial, electric dipole mode of the nanocup to deviate substantially from its characteristic cos2 θ free space scattering profile, while the transverse, magnetic dipole mode remains remarkably insensitive to the presence of the substrate. Nanoscale irregularities of the nanocup rim and the local substrate permittivity have a surprisingly large effect on the spectral- and angle-dependent light-scattering properties of these structures.