Generalizing a method presented in an earlier paper, we express the complex potentials E and Phi of all stationary axisymmetric electrovac spacetimes that correspond to axis data of the form E(z,0) = (U-W)/(U+W) , Phi(z,0) = V/(U+W) , where U = z^2 + U_1 z + U_2 , V = V_1 z + V_2 , W = W_1 z + W_2 , in terms of the complex parameters U_1, V_1, W_1, U_2, V_2 and W_2, that are directly associated with the various multipole moments. (Revised to clarify certain subtle points.)