  We improve the determination of the Higgs-boson mass in the MSSM with heavy
superpartners, by computing the two-loop threshold corrections to the quartic
Higgs coupling that involve both the strong and the electroweak gauge
couplings. Combined with earlier results, this completes the calculation of the
two-loop QCD corrections to the quartic coupling at the SUSY scale. We also
compare different computations of the relation between the quartic coupling and
the pole mass of the Higgs boson at the EW scale. We find that the numerical
impact of the new corrections on the prediction for the Higgs mass is modest,
but comparable to the accuracy of the Higgs-mass measurement at the LHC.
