  We study the optimal use of third order statistics in the analysis of weak
lensing by large-scale structure. These higher order statistics have long been
advocated as a powerful tool to break measured degeneracies between
cosmological parameters. Using ray-tracing simulations, incorporating important
survey features such as a realistic depth-dependent redshift distribution, we
find that a joint two- and three-point correlation function analysis is a much
stronger probe of cosmology than the skewness statistic. We compare different
observing strategies, showing that for a limited survey time there is an
optimal depth for the measurement of third-order statistics, which balances
statistical noise and cosmic variance against signal amplitude. We find that
the chosen CFHTLS observing strategy was optimal and forecast that a joint two-
and three-point analysis of the completed CFHTLS-Wide will constrain the
amplitude of the matter power spectrum $\sigma_8$ to 10% and the matter density
parameter $\Omega_m$ to 17%, a factor of ~2.5 improvement on the two-point
analysis alone. Our error analysis includes all non-Gaussian terms, finding
that the coupling between cosmic variance and shot noise is a non-negligible
contribution which should be included in any future analytical error
calculations.
