  We propose, for the computation of the Higgs mass spectrum and couplings, a
renormalization-group improved leading-log approximation, where the
renormalization scale is fixed to the top-quark pole mass. For the case
$m_A\sim M_{\rm SUSY}$, our leading-log approximation differs by less than 2
GeV from previous results on the Higgs mass computed using a nearly scale
independent renormalization-group improved effective potential up to
next-to-leading order. Moreover, for the general case $m_A\simlt M_{\rm SUSY}$,
we provide analytical formulae (including two-loop leading-log corrections) for
all the masses and couplings in the Higgs sector. For $M_{\rm SUSY}\simlt 1.5$
TeV and arbitrary values of $m_A$, $\tan\beta$ and the stop mixing parameters,
they reproduce the numerical renormalization-group improved leading-log result
for the Higgs masses with an error of less than 3 GeV. For the Higgs couplings,
our analytical formulae reproduce the numerical results equally well.
Comparison with other methods is also performed.
