Precision measurements of the 125 GeV Higgs resonance recently discovered atthe LHC have determined that its properties are similar to the ones of theStandard Model (SM) Higgs boson. However, the current uncertainties in thedetermination of the Higgs boson couplings leave room for significantdeviations from the SM expectations. In fact, if one assumes no correlationbetween the top-quark and gluon couplings to the Higgs, the current global fitto the Higgs data lead to central values of the Higgs couplings to thebottom-quark and the top-quark that are about 2 $\sigma$ away from the SMpredictions. In a previous work, we showed that such a scenario could berealized in the Next to Minimal Supersymmetric extension of the SM (NMSSM), forheavy singlets and light MSSM-like Higgs bosons and scalar top quarks, but forcouplings that ruined the perturbative consistency of the theory up to the GUTscale. In this work we show that a perturbative consistent scenario, forsomewhat heavier stops, may be obtained in the presence of light singlets. Aninteresting bonus of this scenario is the possibility of explaining an excessof events observed in CP-even Higgs searches at LEP2.