  We examine the extent to which it is possible to realize the NMSSM "ideal
Higgs" models espoused in several papers by Gunion et al in the context of
partially universal GUT scale boundary conditions. To this end we use the
powerful methodology of nested sampling. We pay particular attention to whether
ideal-Higgs-like points not only pass LEP constraints but are also acceptable
in terms of the numerous constraints now available, including those from the
Tevatron and $B$-factory data, $(g-2)_\mu$ and the relic density $\Omega h^2$.
In general for this particular methodology and range of parameters chosen, very
few points corresponding to said previous studies were found, and those that
were found were at best $2\sigma$ away from the preferred relic density value.
Instead, there exist a class of points, which combine a mostly singlet-like
Higgs with a mostly singlino-like neutralino coannihilating with the lightest
stau, that are able to effectively pass all implemented constraints in the
region $80<m_h<100$. It seems that the spin-independent direct detection cross
section acts as a key discriminator between ideal Higgs points and the hard to
detect singlino-like points.
