  Band-power estimates of cosmic microwave background fluctuations are now
routinely used to place constraints on cosmological parameters. For this to be
done in a rigorous fashion, the full likelihood function of band-power
estimates must be employed. Even for Gaussian theories, this likelihood
function is not itself Gaussian, for the simple reason that band-powers measure
the {\em variance} of the random sky fluctuations. In the context of Gaussian
sky fluctuations, we use an ideal situation to motivate a general form for the
full likelihood function from a given experiment. This form contains only two
free parameters, which can be determined if the 68% and 95% confidence
intervals of the true likelihood function are known. The ansatz works
remarkably well when compared to the complete likelihood function for a number
of experiments. For application of this kind of approach, we suggest that in
the future both 68% and 95% (and perhaps also the 99.7%) confidence intervals
be given when reporting experimental results.
