We study a region in the NMSSM parameter space in which the mass of the SM-like Higgs boson is uplifted by ∼ 4 − 17 GeV, allowing for stop masses and |A t | ≤ 1 TeV alleviating the little fine tuning problem of the MSSM. An uplift of the mass of the SM-like Higgs boson is possible in two distinct regions in the NMSSM parameter space: Either for large λ and small tan β or, through singlet-doublet mixing, for small λ and large tan β. For a mostly singlet-like Higgs state H S with a mass below 125 GeV we investigate possible direct or indirect search channels at the run II of the LHC as function of the NMSSM-specific uplift of the mass of the SM-like Higgs boson: Direct production of H S in gluon fusion with H S decaying into diphotons, modified reduced couplings of the SM-like Higgs state, and the possible production of H S in ggF → A → Z + H S . We find that the region featuring singlet-doublet mixing can be tested if searches at the LHC at 13 TeV for BSM Higgs bosons in the mass range 88 − 102 GeV decaying into diphotons become sensitive to signal cross sections σ(gg → H S → γγ) ∼ 20 fb, or if measurements of the reduced coupling κ V (H SM ) of the SM Higgs boson to electroweak gauge boson exclude (or confirm) the region κ V (H SM ) < ∼ 0.93.