  Estimation of the angular power spectrum of the Cosmic Microwave Background
(CMB) on a small patch of sky is usually plagued by serious spectral leakage,
specially when the map has a hard edge. Even on a full sky map, point source
masks can alias power from large scales to small scales producing excess
variance at high multipoles. We describe a new fast, simple and local method
for estimation of power spectra on small patches of the sky that minimizes
spectral leakage and reduces the variance of the spectral estimate. For
example, when compared with the standard uniform sampling approach on a 8
degree X 8 degree patch of the sky with 2% area masked due to point sources,
our estimator halves the errorbars at l=2000 and achieves a more than fourfold
reduction in errorbars at l=3500. Thus, a properly analyzed experiment will
have errorbars at l=3500 equivalent to those of an experiment analyzed with the
now standard technique with ~ 16-25 times the integration time.
