In this work, we evaluate the potential of a modeling approach for describing the solid-fluid equilibria of highly asymmetric mixtures over a wide pressure range. The model uses a mathematical expression for the fugacity of a pure heavy compound in solid state for which the reference state is the saturated solid under conditions of solid-liquid (melting) equilibrium at: the system temperature T. Such a reference state differs from a common choice, which corresponds to the pure solid under conditions of solid-vapor (sublimation) equilibrium at T. By construction, the present modeling approach matches the solid-liquid equilibria at high concentration of the heavy component. We discuss and test here a parametrization strategy for avoiding the simultaneous correlation of fluid-fluid and solid-fluid experimental data: first, the fluid-fluid equilibrium experimental data are correlated in the conventional way, and next, the solid-fluid equilibrium data are correlated by fitting a parameter that has no influence on the equation of state that describes the fluid phases. In this work, we study in detail the highly asymmetric system methane + n-triacontane, for which experimental data are available over a wide range of conditions (Machado, J.J.B.; de Loos, T.W. Liquid-vapour and solid-fluid eqiuilibria for the system methane + triacontane at high temperature and high pressure. Fluid Phase Equilib. 2004, 222-223, 261-267). To model this system, we use a specific form of the present modeling approach. Such a specific model gives a good quantitative performance even at pressures in the order of 2000 bar. We also present additional modeling results for two other systems, i.e., for methane + n-eicosane and methane + n-tetracosane, which are also highly asymmetric.