  We discuss various improvements of the prediction for the light MSSM Higgs
boson mass in the hybrid framework of the public code FeynHiggs, which combines
fixed-order and effective field theory results. First, we discuss the
resummation of logarithmic contributions proportional to the bottom-Yukawa
coupling including two-loop $\Delta_b$ resummation. For large $\tan\beta$,
these improvements can lead to large upward shifts of the Higgs mass compared
to the existing fixed-order calculations. Second, we improve the implemented
EFT calculation by fully taking into account the effect of
$\mathcal{CP}$-violating phases. As a third improvement, we discuss the
inclusion of partial N$^3$LL resummation. The presented improvements will be
implemented into FeynHiggs.
