  Assuming that supersymmetry exists well above the weak scale, we derive the
full one-loop matching conditions between the SM and the supersymmetric theory,
allowing for the possibility of an intermediate Split-SUSY scale. We also
compute two-loop QCD corrections to the matching condition of the Higgs quartic
coupling. These results are used to improve the calculation of the Higgs mass
in models with high-scale supersymmetry or split supersymmetry, reducing the
theoretical uncertainty. We explore the phenomenology of a mini-split scenario
with gaugino masses determined by anomaly mediation. Depending on the value of
the higgsino mass, the theory predicts a variety of novel possibilities for the
dark-matter particle.
