  We aim to improve the surface of last scattering (SLS) optimal
cross-correlation method in order to refine estimates of the Poincar\'e
dodecahedral space (PDS) cosmological parameters. We analytically derive the
formulae required to exclude points on the sky that cannot be members of close
SLS-SLS cross-pairs. These enable more efficient pair selection without
sacrificing uniformity of the underlying selection process. In certain cases
this decreases the calculation time and increases the number of pairs per
separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the
five-year WMAP data; and (ii) we seek PDS solutions in a small number of
Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a
calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS
parameters for the five-year WMAP data are similar to those for the three-year
data. (ii) Comparison of the optimal solutions found by the MCMC chains in the
observational map to those found in the simulated maps yields a slightly
stronger rejection of the simply connected model using $\alpha$ than using the
twist angle $\phi$. The best estimate of $\alpha$ implies that_given a large
scale auto-correlation as weak as that observed,_ the PDS-like
cross-correlation signal in the WMAP data is expected with a probability of
less than about 10%. The expected distribution of $\phi$ from the GRF
simulations is approximately Gaussian around zero, it is not uniform on
$[-\pi,\pi]$. We infer that for an infinite, flat, cosmic concordance model
with Gaussian random fluctuations, the chance of finding_both_ (a) a large
scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal
similar to that observed is less than about 0.015% to 1.25%.
