  In the motivated hypothesis that the scalar bosons of the Next-to-Minimal
Supersymmetric Standard Model (NMSSM) be the lightest new particles around, a
possible strategy to search for signs of the extra CP-even states is outlined.
It is shown how the measurements of the couplings of the 126 GeV Higgs boson
constrain the region of the physical parameters in a generic NMSSM which
minimises the fine-tuning of the electroweak scale. We also determine the cross
section for the production of a heavier CP-even scalar, together with its most
relevant branching ratios.
