The MSA/MSA solution of the wall-particle Ornstein–Zernike equation for the one-component plasma is formulated as a fastly convergent expansion, convenient for numerical calculations, which avoids the usual zone-by-zone representation of the profile ρ(z). ρ(z) is then a sum of exponential terms of complex arguments tn, where the tn are the zeros of the Baxter function Q̃(k). A typical relation between the contact value ρ(o), the total potential drop, and the isothermal compressibility is derived. This new treatment of the MSA/MSA equation is used to extend previous work in two directions: (i) the wall is placed at an arbitrary distance from the edge of the background profile; and (ii) the ions and the background interact via a pseudopotential. The influence of the pseudopotential radius is discussed numerically and the free-surface situation is also considered. The effect of the pseudopotential is formally equivalent to the introduction of an adsorption potential at the wall.