  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 lambda and small
tan(beta) or, through singlet-doublet mixing, for small lambda and large
tan(beta). 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 sigma(gg -> H_S -> diphotons) ~ 20
fb, or if measurements of the reduced coupling kappa_V(H_{SM}) of the SM Higgs
boson to electroweak gauge boson exclude (or confirm) the region
kappa_V(H_{SM}) <~ 0.93.
