  A multicanonical update relation for calculation of the microcanonical
entropy $S_{micro}(E)$ by means of the estimates of the inverse statistical
temperature $\beta_S$, is proposed. This inverse temperature is obtained from
the recently proposed statistical temperature weighted histogram analysis
method (ST-WHAM). The performance of ST-WHAM concerning the computation of
$S_{micro}(E)$ from canonical measures, in a model with strong free-energy
barriers, is also discussed on the basis of comparison with the multicanonical
simulation estimates.
