  We consider the fully constrained version of the next-to-minimal
supersymmetric extension of the standard model (cNMSSM) in which a singlet
Higgs superfield is added to the two doublets that are present in the minimal
extension (MSSM). Assuming universal boundary conditions at a high scale for
the soft supersymmetry-breaking gaugino, sfermion and Higgs mass parameters as
well as for the trilinear interactions, we find that the model is more
constrained than the celebrated minimal supergravity model. The
phenomenologically viable region in the parameter space of the cNMSSM
corresponds to a small value for the universal scalar mass m_0: in this case,
one single input parameter is sufficient to describe the phenomenology of the
model once the available constraints from collider data and cosmology are
imposed. We present the particle spectrum of this very predictive model and
discuss how it can be distinguished from the MSSM.
