  In MSSM models with various boundary conditions for the soft breaking terms
(m_{soft}) and for a higgs mass of 126 GeV, there is a (minimal) electroweak
fine-tuning Delta\approx 800 to 1000 for the constrained MSSM and Delta\approx
500 for non-universal gaugino masses. These values, often regarded as
unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking,
rather than of SUSY itself. A minimal modification of these models is to lower
the SUSY breaking scale in the hidden sector (\sqrt f) to few TeV, which we
show to restore naturalness to more acceptable levels Delta\approx 80 for the
most conservative case of low tan_beta and ultraviolet boundary conditions as
in the constrained MSSM. This is done without introducing additional fields in
the visible sector, unlike other models that attempt to reduce Delta. In the
present case Delta is reduced due to additional (effective) quartic higgs
couplings proportional to the ratio m_{soft}/(\sqrt f) of the visible to the
hidden sector SUSY breaking scales. These couplings are generated by the
auxiliary component of the goldstino superfield. The model is discussed in the
limit its sgoldstino component is integrated out so this superfield is realized
non-linearly (hence the name of the model) while the other MSSM superfields are
in their linear realization. By increasing the hidden sector scale \sqrt f one
obtains a continuous transition for fine-tuning values, from this model to the
usual (gravity mediated) MSSM-like models.
