  We consider the QCD corrections to the electric dipole moment of the neutron
in the Minimal Supersymmetric Standard Model. We provide a master formula for
the Wilson coefficients at the low energy scale including for the first time
the mixing between the electric and chromoelectric operators and correcting
widely used previous LO estimates. We show that, because of the mixing between
the electric and chromoelectric operators, the neutralino contribution is
always strongly suppressed. We find that, in general, the effect of the QCD
corrections is to reduce the amount of CP violation generated at the high
scale. We discuss the perturbative uncertainties of the LO computation, which
are particularly large for the gluino-mediated contribution. This motivates our
Next-to-Leading order analysis. We compute for the first time the order alpha_s
corrections to the Wilson coefficients for the gluino contributions, and
recompute the two-loop anomalous dimension for the dipole operators. We show
that the large LO uncertainty disappears once NLO corrections are taken into
account.
