  Precision measurements of the 125 GeV Higgs resonance recently discovered at
the LHC have determined that its properties are similar to the ones of the
Standard Model (SM) Higgs boson. However, the current uncertainties in the
determination of the Higgs boson couplings leave room for significant
deviations from the SM expectations. In fact, if one assumes no correlation
between the top-quark and gluon couplings to the Higgs, the current global fit
to the Higgs data lead to central values of the Higgs couplings to the
bottom-quark and the top-quark that are about 2 $\sigma$ away from the SM
predictions. In a previous work, we showed that such a scenario could be
realized in the Next to Minimal Supersymmetric extension of the SM (NMSSM), for
heavy singlets and light MSSM-like Higgs bosons and scalar top quarks, but for
couplings that ruined the perturbative consistency of the theory up to the GUT
scale. In this work we show that a perturbative consistent scenario, for
somewhat heavier stops, may be obtained in the presence of light singlets. An
interesting bonus of this scenario is the possibility of explaining an excess
of events observed in CP-even Higgs searches at LEP2.
