Escaping the Large Fine-Tuning and Little Hierarchy Problems in the Next to Minimal Supersymmetric Model andh→aaDecays

We demonstrate that the next to minimal supersymmetric model can have small fine-tuning and modest top-squark mass while still evading all experimental constraints. For small $\tan \beta$ (large $\tan \beta$), the relevant scenarios are such that there is always (often) a standard-model-like Higgs boson that decays to two lighter—possibly much lighter—Higgs pseudoscalars.