Unidirectional magnetic anisotropies in low-symmetry magnetic thin films such as cobalt on vicinal copper surfaces are investigated. Possible explanations of the observed uniaxial anisotropies are competing anisotropy (CA) coefficients and Dzyaloshinskii-Moriya (DM) interactions. Unidirectional CA is an interesting mechanism occurring in low-symmetry magnets and involves neither antiferromagnetic exchange nor spin canting. It is visible in the easy-cone regime and decides, for example, whether the preferential magnetization direction points up or down a stepped surface. In the case of Co/Cu(11n) films, however, the anisotropy direction speaks in favor of DM-type interactions.