Critical lines of a two-component gas-liquid system can be plotted as a function of temperature and pressure, as is usually done with experimental results, and also as a function of the density coordinates. In the latter representation the mathematical double points can be found with higher precision. The existence of such a point depends on the values of the energy parameters, and the locus of these parameter values giving rise to double points maps the boundary between the different kinds of phase diagram. We show how the double point, which in the case of the lattice gas is due to an accidental symmetry, can be regained in various other, less symmetrical models by adjustment of the inter-action parameters.