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 dat
a of the MAXIMA-1 experiment, where the asymmetry is mild. We show that in
both cases the formalism does not bias the angular power spectrum estimates
. We analyze the limitations of the formalism and find that it is well suit
ed for most practical situations.