We propose a new formalism to handle asymmetric beams in the data analysis of cosmic microwave background anisotropy experiments. For any beam shape, the formalism finds the optimal circularly symmetric equivalent and is thus easily adaptable to existing data analysis methods. We demonstrate certain key points by using a simulated highly elliptic beam and the beams and data of the MAXIMA-1 experiment, where the asymmetry is mild. We show that in both cases the formalism does not bias the angu...