By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek-type theories, which remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye-Hückel theory. The screening length consistent with the non-electrostatic terms in the free energy ansatz for the Flory-Huggins and Voorn-Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some special cases.