The predictions of the crystallization temperature and the amount of precipitates of paraffin waxes at high pressure conditions may be inaccurate using existing thermodynamic models. This is mainly due to the lack of experimental data on the molar volume of solid paraffins at high pressures. This inaccuracy is even more pronounced for mixtures of high asymmetry. The present work provides a new accurate modeling approach for solid fluid equilibrium (SFE) at high pressure conditions, more specifically, for highly asymmetric systems. In contrast to the conventional methods for high pressure SFE modeling which define a Poynting molar volume correction term to calculate the paraffin solid phase nonideality at high pressures, the new method exploits the values of thermophysical properties of importance in SFE modeling (temperatures and enthalpies of fusion and solid solid transition) evaluated at the high pressure condition using a new insight into the well-known Clausius-Clapeyron equation. These modified parameters are then used for evaluation of the fugacity in the solid phase at higher pressure using the fugacity of pure liquid at the same pressure and applying the well-established formulation of the Gibbs energy change during melting. Therefore, the devised approach does not require a Poynting correction term. The devised approach coupled with the well-tested UNIQUAC activity coefficient model is used to describe the nonideality of the solid phase. For the fluid phases, the fugacities are obtained with the SRK EoS with binary interaction parameters calculated with a group contribution scheme. The-model is applied to highly asymmetric systems with SFE experimental data over a wide range of pressures. It is first used to predict crystallization temperature in binary systems at high pressures and then verified by applying it on multicomponent mixtures resembling intermediate oil and natural gas condensates.