  We present several advances in the effective field theory calculation of the
Higgs mass in MSSM scenarios with heavy superparticles. In particular, we
compute the dominant two-loop threshold corrections to the quartic Higgs
coupling for generic values of the relevant SUSY-breaking parameters, including
all contributions controlled by the strong gauge coupling and by the
third-family Yukawa couplings. We also study the effects of a representative
subset of dimension-six operators in the effective theory valid below the SUSY
scale. Our results will allow for an improved determination of the Higgs mass
and of the associated theoretical uncertainty.
