  This paper generalises the hybrid power spectrum estimator developed in
Efstathiou (2004a) to the estimation of polarization power spectra of the
cosmic microwave background radiation. The hybrid power spectrum estimator is
unbiased and we show that it is close to optimal at all multipoles, provided
the pixel noise satisfies certain reasonable constraints. Furthermore, the
hybrid estimator is computationally fast and can easily be incorporated in a
Monte-Carlo chain for Planck-sized data sets. Simple formulae are given for the
covariance matrices, including instrumental noise, and these are tested
extensively against numerical simulations. We compare the behaviour of simple
pseudo-Cell estimates with maximum likelihood estimates at low multipoles. For
realistic sky cuts, maximum likelihood estimates reduce very significantly the
mixing of E and B modes. To achieve limits on the scalar-tensor ratio of r<<0.1
from sky maps with realistic sky cuts, maximum likelihood methods, or
pseudo-Cell estimators based on unambiguous E and B modes, will be essential.
