of heuristic weighting that are peculiar to polarization analysis, particularly $E$-$B$ mixing. An obvious extension of this work that will be required for application to real data is to include the contribution from instrument noise. For uncorrelated noise this should be straightforward, but in a more realistic set-up, one will probably have to resort to Monte-Carlo simulations for the noise contribution.

As noted above, one of the future goals of CMB polarization observations is to detect (or constrain) the stochastic gravitational wave background via its signature in large-angle $B$-mode polarization [@seljak97; @kamionkowski97]. Magnetic polarization allows much smaller amplitude gravitational wave backgrounds to be detected than with temperature or electric polarization alone, since, in the latter case, the gravitational-wave signal is swamped by the cosmic variance of the signal from the dominant density perturbations. Methods to separate out exactly pure magnetic modes from observations with incomplete sky coverage exist at the map level [@lewis02; @bunn03; @lewis03]. Such methods have the desirable property that quadratic power spectrum estimates formed from the pure-$B$ modes have no cosmic variance if the $B$-mode power is zero. Were it not for gravitational lensing, separating $B$ modes at the level of the map would thus allow the 