  Dominant energy subspaces of statistical systems are defined with the help of
restrictive conditions on various characteristics of the energy distribution,
such as the probability density and the forth order Binder's cumulant. Our
analysis generalizes the ideas of the critical minimum energy-subspace (CrMES)
technique \cite{malakis04}, applied previously to study the specific heat's
finite-size scaling. Here, we illustrate alternatives that are useful for the
analysis of further finite-size anomalies and the behavior of the corresponding
dominant subspaces is presented for the 2D Baxter-Wu, the 2D and 3D Ising
models. In order to show that a CrMES technique is adequate for the study of
magnetic anomalies, we study and test simple methods which provide the means
for an accurate determination of the energy - order-parameter ($E-M$)
histograms via Wang-Landau random walks. The 2D Ising model is used as a test
case and it is shown that high-level Wang-Landau sampling schemes yield
excellent estimates for all magnetic properties. Our estimates compare very
well with those of the traditional Metropolis method. The relevant dominant
energy subspaces and dominant magnetization subspaces scale as expected with
exponents $\alpha/\nu$ and $\gamma/\nu$ respectively. Using the Metropolis
method we examine the time evolution of the corresponding dominant
magnetization subspaces and we uncover the reasons behind the inadequacy of the
Metropolis method to produce a reliable estimation scheme for the tail-regime
of the order parameter distribution.
