  We explore the low-l likelihood of the angular spectrum C(l) of masked CMB
temperature maps using an adaptive importance sampler. We find that, in spite
of a partial sky coverage, the likelihood distribution of each C(l) closely
follows an inverse gamma distribution. Our exploration is accurate enough to
measure the inverse gamma parameters along with the correlation between
multipoles. Those quantities are used to build an approximation of the joint
posterior distribution of the low-l likelihood. The accuracy of the proposed
approximation is established using both statistical criteria and a mock
cosmological parameter fit. When applied to the WMAP5 data set, this
approximation yields cosmological parameter estimates at the same level of
accuracy as the best current techniques but with very significant speed gains.
