  We discuss the conceptual differences between the Broad Histogram (BHM) and
reweighting methods in general, and particularly the so-called Multicanonical
(MUCA) approaches. The main difference is that BHM is based on microcanonical,
fixed-energy averages which depends only on the good statistics taken {\bf
inside} each energy level. The detailed distribution of visits among different
energy levels, determined by the particular dynamic rule one adopts, is
irrelevant. Contrary to MUCA, where the results are extracted from the dynamic
rule itself, within BHM any microcanonical dynamics could be adopted. As a
numerical test, we have used both BHM and MUCA in order to obtain the spectral
energy degeneracy of the Ising model in $4 \times 4 \times 4$ and $32 \times
32$ lattices, for which exact results are known. We discuss why BHM gives more
accurate results than MUCA, even using {\bf the same} Markovian sequence of
states. In addition, such advantage increases for larger systems.
