  In supersymmetric extensions of the Standard Model, superpartner masses
consistent with collider bounds typically introduce significant tuning of the
electroweak scale. We show that hidden sector renormalisation can greatly
reduce such a tuning if the supersymmetry breaking, or mediating, sector runs
through a region of strong coupling not far from the weak scale. In the
simplest models, only the tuning due to the gaugino masses is improved, and a
weak scale gluino mass in the region of 5 TeV may be obtained with an
associated tuning of only one part in ten. In models with more complex
couplings between the visible and hidden sectors, the tuning with respect to
sfermions can also be reduced. We give an example of a model, with low scale
gauge mediation and superpartner masses allowed by current LHC bounds, that has
an overall tuning of one part in twenty.
