  In a recent paper arXiv:1107.5048, we discussed the correlation between the
elastic neutralino-nucleon scattering cross section, constrained by dark matter
direct detection experiments, and fine-tuning at tree-level in the electroweak
symmetry breaking sector of the Minimal Supersymmetric Standard Model (MSSM).
Here, we show that the correlation persists in the Next-to-Minimal
Supersymmetric Standard Model (NMSSM), and its variant, lambda-SUSY. Both
models are strongly motivated by the recent discovery of a 125 GeV Higgs-like
particle. We also discuss the implications of the recently published bound on
the direct detection cross section from 225 live days of XENON100 experiment.
In both the MSSM and the NMSSM, most of the parameter space with fine-tuning
less than 10% is inconsistent with the XENON100 bound. In lambda-SUSY, on the
other hand, large regions of completely natural electroweak symmetry breaking
are still allowed, primarily due to a parametric suppression of fine-tuning
with large \lambda. The upcoming XENON1T experiment will be able to probe most
of the parameter space with less than 1% fine-tuning in all three models.
