  In the era of high precision CMB measurements, systematic effects are
beginning to limit the ability to extract subtler cosmological information. The
non-circularity of the experimental beam has become progressively important as
CMB experiments strive to attain higher angular resolution and sensitivity. The
effect of non-circular beam on the power spectrum is important at multipoles
larger than the beam-width. For recent experiments with high angular
resolution, optimal methods of power spectrum estimation are computationally
prohibitive and sub-optimal approaches, such as the Pseudo-Cl method, are used.
We provide an analytic framework for correcting the power spectrum for the
effect of beam non-circularity and non-uniform sky coverage (including
incomplete/masked sky maps). The approach is perturbative in the distortion of
the beam from non-circularity allowing for rapid computations when the beam is
mildly non-circular. When non-circular beam effect is important, we advocate
that it is computationally advantageous to employ `soft' azimuthally apodized
masks whose spherical harmonic transform die down fast with m.
