  We calculate the CMB anisotropy in compact hyperbolic universe models using
the regularized method of images described in paper-I, including the
'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering
surface terms. We calculate the Bayesian probabilities for a selection of
models by confronting our theoretical pixel-pixel temperature correlation
functions with the COBE-DMR data. Our results demonstrate that strong
constraints on compactness arise: if the universe is small compared to the
`horizon' size, correlations appear in the maps that are irreconcilable with
the observations. This conclusion is qualitatively insensitive to the matter
content of the universe, in particular, the presence of a cosmological
constant. If the universe is of comparable size to the 'horizon', the
likelihood function is very dependent upon orientation of the manifold wrt the
sky. While most orientations may be strongly ruled out, it sometimes happens
that for a specific orientation the predicted correlation patterns are
preferred over those for the conventional infinite models. The full Bayesian
analysis we use is the most complete statistical test that can be done on the
COBE maps, taking into account all possible signals and their variances in the
theoretical skies, in particular the high degree of anisotropic correlation
that can exist. We show that standard visual measures for comparing theoretical
predictions with the data such as the isotropized power spectrum $C_\ell$ are
not so useful in small compact spaces because of enhanced cosmic variance
associated with the breakdown of statistical isotropy.
