  We propose a new recursive procedure to estimate the microcanonical density
of states in multicanonical Monte Carlo simulations which relies only on
measurements of moments of the energy distribution, avoiding entirely the need
for energy histograms. This method yields directly a piecewise analytical
approximation to the microcanonical inverse temperature, $\beta(E)$, and allows
improved control over the statistics and efficiency of the simulations. We
demonstrate its utility in connection with recently proposed schemes for
improving the efficiency of multicanonical sampling, either with adjustment of
the asymptotic energy distribution or with the replacement of single spin flip
dynamics with collective updates.
