  The minimal supersymmetric standard model leads to precise predictions of the
properties of the light Higgs boson degrees of freedom that depend on only a
few relevant supersymmetry breaking parameters. In particular, there is an
upper bound on the mass of the lightest neutral Higgs boson, which for a
supersymmetric spectrum of the order of a TeV is barely above the one of the
Higgs resonance recently observed at the LHC. This bound can be raised by
considering a heavier supersymmetric spectrum, relaxing the tension between
theory and experiment. In a previous article, we studied the predictions for
the lightest CP-even Higgs mass for large values of the scalar-top and heavy
Higgs boson masses. In this article we perform a similar analysis, considering
also the case of a CP-odd Higgs boson mass $m_A$ of the order of the weak
scale. We perform the calculation using effective theory techniques,
considering a two-Higgs doublet model and a Standard Model-like theory and
resumming the large logarithmic corrections that appear at scales above and
below $m_A$, respectively. We calculate the mass and couplings of the lightest
CP-even Higgs boson and compare our results with the ones obtained by other
methods.
