  We study the phenomenology of a new Minimally-extended Supersymmetric
Standard Model (nMSSM) where a gauge singlet superfield is added to the MSSM
spectrum. The superpotential of this model contains no dimensionful parameters,
thus solving the mu-problem of the MSSM. A global discrete R-symmetry,
forbidding the cubic singlet self-interaction, imposed on the complete theory,
guarantees its stability with respect to generated higher-order tadpoles of the
singlet and solves both the domain wall and Peccei-Quinn axion problems. We
give the free parameters of the model and display some general constraints on
them. A particular attention is devoted to the neutralino sector where a
(quasi-pure) singlino appears to be always the LSP of the model, leading to
additional cascades, involving the NLSP -> LSP transition, compared with the
MSSM. We then present the upper bounds on the masses of the lightest and
next-to-lightest -- when the lightest is an invisible singlet -- CP-even Higgs
bosons, including the full one-loop and dominant two-loop corrections. These
bounds are found to be much higher than the equivalent ones in the MSSM.
Finally, we discuss some phenomenological implications for the Higgs sector of
the nMSSM in Higgs production at future hadron colliders.
