brute-force maximum likelihood (e.g. @gorski94 [@bond98]), and its quadratic approximation [@tegmark02], should produce the most accurate (minimum-variance) estimates. However, these methods require the inversion of $N_{\rmn{pix}}\times N_{\rmn{pix}}$ matrices, where $N_{\rmn{pix}}$ is the number of pixels in the map, which is prohibitively slow for the analysis of mega-pixel maps. Given these limitations, a number of fast alternative methods have been suggested [@hansen02b; @kogut03; @chon04] building on earlier work on the analysis of the temperature anisotropies [@szapudi01; @wandelt01b; @hivon02; @hansen02]. These fast methods are closely related, and all involve compressing heuristically-weighted maps of the Stokes parameters into a set of pseudo-$C_l$s making use of spherical transforms – a step that requires only $O(N_{\rmn{pix}}^{3/2})$ operations with fast Fourier transform methods on iso-latitude pixelisations such as the widely-used HEALPix [@gorski04]. The methods differ in the details of how they transform the pseudo-$C_l$s to power spectrum estimates. In the absence of instrument noise, the mean of the pseudo-$C_l$s is linear in the true power spectra, so, for observations over a large enough part of the sky, unbiased power spectrum estimates can be obtained by applying the inverse operation to the pseudo-$C_l$s [@kogut03]. If the observed part of the sky is sufficiently small, direct inversion is 