  We present an efficient method of reconstructing the parameters of the
Constrained MSSM from assumed future LHC data, applied both on their own right
and in combination with the cosmological determination of the relic dark matter
abundance. Focusing on the ATLAS SU3 benchmark point, we demonstrate that our
simple Gaussian approximation can recover the values of its parameters
remarkably well. We examine two popular non-informative priors and obtain very
similar results, although when we use an informative, naturalness-motivated
prior, we find some sizeable differences. We show that a further strong
improvement in reconstructing the SU3 parameters can by achieved by applying
additional information about the relic abundance at the level of WMAP accuracy,
although the expected data from Planck will have only a very limited additional
impact. Further external data may be required to break some remaining
degeneracies. We argue that the method presented here is applicable to a wide
class of low-energy effective supersymmetric models, as it does not require to
deal with purely experimental issues, eg, detector performance, and has the
additional advantages of computational efficiency. Furthermore, our approach
allows one to distinguish the effect of the model's internal structure and of
the external data on the final parameters constraints.
