Fawcett and Henderson [J. Phys. Chem B, 104 (2000) 6837] have developed a simple treatment of the electrical double layer that is based on the Poisson-Boltzmann theory of Gouy and Chapman but modified in the light of an exact result. They called the approach a generalized mean spherical approximation even though the approach is only loosely connected with the mean spherical approximation. In their paper, this approach was tested by comparison with simulation results for aqueous monovalent electrolytes at room temperature, where the electrostatic coupling is relatively weak, and was found to be very satisfactory. Here, we test the underlying conjecture of this approach for electrolytes in which the electrostatic coupling between the ions is strong. We also propose a modification of this conjecture. We find that these conjectures and some consequences agree qualitatively with simulations of a double layer formed by an electrolyte that is near its critical point. (C) 2004 Elsevier B.V. All rights reserved.