We employ both the minimal gravity- and the minimal gauge mediations of supersymmetry breaking at the grand unified theory (GUT) scale in a single supergravity framework, assuming the gaugino masses are generated dominantly by the minimal gauge mediation effects. In such a minimal mixed mediation model, a focus point of the soft Higgs mass parameter, m_{h_u}^2 emerges at 3-4 TeV energy scale, which is exactly the stop mass scale needed for explaining the 126 GeV Higgs boson mass without the A-term at the three loop level. As a result, m_{h_u}^2 in the MSSM can be quite insensitive to various trial stop masses at low energy, reducing the fine-tuning measures to be much smaller than 100 even for a 3-4 TeV low energy stop mass and -0.5 < A_t / m_0 < +0.1 at the GUT scale. The $mu$ parameter is smaller than 600 GeV. The gluino mass is predicted to be about 1.7 TeV, which could readily be tested at LHC run2.
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