The primitive model for electrolytes constituted by asymmetric dimers (two charged spheres of arbitrary radii in contact) in a continuous solvent is treated in the variational mean spherical scaling approximation, a generalization of the mean spherical approximation. These theories are extensions of the linearized Poisson-Boltzmann (or Debye-Huckel) approximation that take into account the excluded volume effect of all the ions in the solution. The variational mean spherical scaling approximation is derived from a variational principle in which the energy is obtained from simple electrostatic considerations, and where the entropy is a universal function. We show that this approximation yields the correct limiting thermodynamics for both low and high concentration for ions of arbitrary shape. This work is an extension of our previously presented treatment for symmetric dimers. (C) 2003 American Institute of Physics.