  We have developed a fast, accurate and generally applicable method for
inferring the power spectrum and its uncertainties from maps of the cosmic
microwave background (CMB) in the presence of inhomogeneous and correlated
noise. For maps with 10 to 100 thousand pixels, we apply an exact power
spectrum estimation algorithm to submaps of the data at various resolutions,
and then combine the results in an optimal manner. To analyze larger maps
efficiently one must resort to sub-optimal combinations in which cross-map
power spectrum error correlations are only calculated approximately. We expect
such approximations to work well in general, and in particular for the
megapixel maps to come from the next generation of satellite missions.
