  We present a solution to the gravitino problem, which arises in the NMSSM,
allowing for sparticle spectra from ordinary gravity-mediated supersymmetry
breaking with weak-scale gravitino dark matter. The coupling, which links the
singlet to the MSSM sector, enhances the tree-level Higgs mass, providing an
attractive explanation why the observed Higgs boson is so heavy. The same
coupling induces very efficient pair-annihilation processes of the neutralino
NLSP. Its relic abundance can be sufficiently suppressed to satisfy the strong
constraints on late decaying relics from primordial nucleosynthesis -- even for
very long neutralino lifetimes. The striking prediction of this scenario is the
detection of a pseudoscalar Higgs boson in the search for top-top resonances at
LHC-14, rendering it completely testable.
