  We investigate a particular version of the Peccei-Quinn (PQ) NMSSM
characterized by an economical and rigidly hierarchical flavor structure and
based on flavored gauge mediation and on some considerations inspired by string
theory GUTs. In this way we can express the Lagrangian of the PQ NMSSM through
very few parameters. The obtained model is studied numerically and confronted
with the most relevant phenomenological constraints. We show that typical
spectra are for the most part too heavy to be significantly probed at the LHC,
but regions of the parameter space exist yielding signatures that might
possibly be observed during Run II. We also calculate the fine tuning of the
model. We show that, in spite of the appearance of large scales in the
superpotential and soft terms, it does not exceed the tuning present in the
MSSM for equivalent spectra, which is of the order of 10^4.
