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 fourth order Binder’s cumulant. Our analysis generalizes the ideas of the critical minimum energy subspace (CRMES) technique, 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 two-dimensional (2D) Baxter-Wu and 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 α∕ν and γ∕ν, 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.