  In order to significantly reduce the fine-tuning associated with the
electroweak symmetry breaking in the minimal supersymmetric standard model
(MSSM), we consider not only the minimal gravity mediation effects but also the
minimal gauge mediation ones for a common supersymmetry breaking source at a
hidden sector. In this "Minimal Mixed Mediation model," the minimal forms for
the Kahler potential and the gauge kinetic function are employed at tree level.
The MSSM gaugino masses are radiatively generated through the gauge mediation.
Since a "focus point" of the soft Higgs mass parameter, m_{h_u}^2 appears
around 3-4 TeV energy scale in this case, m_{h_u}^2 is quite insensitive to
stop masses. Instead, the naturalness of the small m_{h_u}^2 is more closely
associated with the gluino mass rather than the stop mass unlike the
conventional scenario. As a result, even a 3-4 TeV stop mass, which is known to
explain the 125 GeV Higgs mass at three-loop level, can still be compatible
with the naturalness of the electroweak scale. On the other hand, the
requirements of various fine-tuning measures much smaller than 100 and |\mu| <
600 GeV constrain the gluino mass to be 1.6 TeV < M_3 < 2.2 TeV, which is
well-inside the discovery potential range of LHC RunII.
