  The unprecedented quality, the increased dataset, and the wide area of
ongoing and near future weak lensing surveys allows to move beyond the standard
two points statistics thus making worthwhile to investigate higher order
probes. As an interesting step towards this direction, we expolore the use of
higher order moments (HOM) of the convergence field as a way to increase the
lensing Figure of Merit (FoM). To this end, we rely on simulated convergence to
first show that HOM can be measured and calibrated so that it is indeed
possible to predict them for a given cosmological model provided suitable
nuisance parameters are introduced and then marginalized over. We then forecast
the accuracy on cosmological parameters from the use of HOM alone and in
combination with standard shear power spectra tomography. It turns out that HOM
allow to break some common degeneracies thus significantly boosting the overall
FoM. We also qualitatively discuss possible systematics and how they can be
dealt with.
