  The observed angular correlation function of the cosmic microwave background
has previously been reported to be anomalous, particularly when measured in
regions of the sky uncontaminated by Galactic emission. Recent work by
Efstathiou et al. presents a Bayesian comparison of isotropic theories, casting
doubt on the significance of the purported anomaly. We extend this analysis to
all anisotropic Gaussian theories with vanishing mean (<delta T> = 0), using
the much wider class of models to confirm that the anomaly is not likely to
point to new physics. On the other hand if there is any new physics to be
gleaned, it results from low-l alignments which will be better quantified by a
full-sky statistic.
  We also consider quadratic maximum likelihood power spectrum estimators that
are constructed assuming isotropy. The underlying assumptions are therefore
false if the ensemble is anisotropic. Nonetheless we demonstrate that, for
theories compatible with the observed sky, these estimators (while no longer
optimal) remain statistically superior to pseudo-C_l power spectrum estimators.
