Escaping the large fine-tuning and little hierarchy problems in the next to minimal supersymmetric model and h --> aa decays

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.