  We examine the use of modified Higgs sectors to address the little hierarchy
problem of supersymmetry. Such models reduce weak-scale fine-tuning by allowing
lighter stops, but they retain some fine-tuning independent of the Higgs. The
modified Higgs sector can also introduce model-dependent tunings. We consider
the model-independent constraints on naturalness from squark, gluino, chargino
and neutralino searches, as well as the model-dependent tuning in the PQ- and
R-symmetric limits of the NMSSM, where cascade decays or additional quartic
interactions can hide a Higgs without relying on heavy stops. Obtaining viable
electroweak symmetry breaking requires a tuning of $\sim 1-10%$ in the PQ
limit. A large A-term is also necessary to make charginos sufficiently heavy,
and this introduces an additional weak-scale tuning of $\sim 10%$. The
R-symmetric limit requires large marginal couplings, a large singlet soft mass,
and a tuning of $\sim 5-10%$ to break electroweak symmetry. Hiding MSSM-like
Higgs states below $\approx 112$ GeV requires additional tunings of A-terms at
the $\sim 1-10%$ level. Thus, although the NMSSM has rich discovery potential,
it suffers from a unique fine-tuning problem of its own.
