The integral equation for isotherms is reviewed in order to select simple, practical, high-performance energy distributions from among the numerous existing models. Adsorption equilibria can be derived from occupation indices of suitable distributed energy levels. For mono sites, the occupation index is a Fermi-Dirac function. Whether a surface is energetically heterogeneous or homogeneous depends on the ratio of the breadth of the energy level distribution a to the thermal fluctuation U. Although, there are only a few energy distributions for which analytic isotherm equations are known, the numerical evaluation shows general properties: the symmetry point Theta = (1)/(2), the temperature domain for real or ideal behaviour and isotherm shapes without extrema. As an example, experimental equilibria of CO at molecular sieve 5A are fitted to a hyperbolic energy distribution using four physical parameters: the reference loading, a reference fluid phase pressure phi(Theta = (1)/(2), T-ref), the mean value and the standard deviation of the adsorption energy level distribution. (c) 2005 Elsevier Ltd. All rights reserved.