  We study the O(at*as + at^2) two-loop corrections to the minimization
conditions of the MSSM effective potential, providing compact analytical
formulae for the Higgs tadpoles. We connect these results with the
renormalization group running of the MSSM parameters from the grand unification
scale down to the weak scale, and discuss the corrections to the Higgs mixing
parameter mu and to the running CP-odd Higgs mass mA in various scenarios of
gravity-mediated SUSY breaking. We find that the O(at*as) and O(at^2)
contributions partially cancel each other in the minimization conditions. In
comparison with the full one-loop corrections, the O(at*as + at^2) two-loop
corrections significantly weaken the dependence of the parameters mu and mA on
the renormalization scale at which the effective potential is minimized. The
residual two-loop and higher-order corrections to mu and mA are estimated to be
at most 1% in the considered scenarios.
