  Powerful constraints on theories can already be inferred from existing CMB
anisotropy data. But performing an exact analysis of available data is a
complicated task and may become prohibitively so for upcoming experiments with
\gtrsim10^4 pixels. We present a method for approximating the likelihood that
takes power spectrum constraints, e.g., ``band-powers'', as inputs. We identify
a bias which results if one approximates the probability distribution of the
band-power errors as Gaussian---as is the usual practice. This bias can be
eliminated by using specific approximations to the non-Gaussian form for the
distribution specified by three parameters (the maximum likelihood or mode,
curvature or variance, and a third quantity). We advocate the calculation of
this third quantity by experimenters, to be presented along with the
maximum-likelihood band-power and variance. We use this non-Gaussian form to
estimate the power spectrum of the CMB in eleven bands from multipole moment
ell = 2 (the quadrupole) to ell=3000 from all published band-power data. We
investigate the robustness of our power spectrum estimate to changes in these
approximations as well as to selective editing of the data.
