Low-temperature oil displacements by CO2 involve complex phase behavior, where three hydrocarbon phases can coexist. Reliable design of miscible gas flooding requires knowledge of the minimum miscibility pressure (MMP), which is the pressure required for 100% recovery in the absence of dispersion or as defined by slim-tube experiments as the "knee" in the recovery curve with pressure where displacement efficiency is greater than 90%. There are currently no analytical methods to estimate the MMP for multicomponent mixtures exhibiting three hydrocarbon phases. Also, there are no reliable numerical methods to estimate the MMP using compositional simulation largely because of robustness issues of three-phase equilibrium calculations, inaccurate three-phase relative permeability models, and phase identification and labeling problems that can cause significant discontinuities and failures in the simulation results. How miscibility is developed, or not developed, for a three-phase displacement is not well known. We developed a new multiple three-phase mixing cell method that gives a relatively easy and robust way to determine the pressure for miscibility or more importantly the pressure for high displacement efficiency. The procedure that moves fluid from cell to cell is robust because it is independent of phase labeling (i.e. vapor or liquid), has a robust way to provide good initial guesses for three-phase flash calculations, and is also not dependent on three-phase relative permeability (fractional flow). These three aspects give the mixing cell approach significant advantages over using compositional simulation to estimate MMP or to understand miscibility development. The approach can be integrated with previously developed twophase multiple mixing cell models because it uses the tie-line lengths from the boundaries of tie triangles to recognize when the MMP or pressure for high displacement efficiency is obtained. Application of the mixing cell algorithm shows that unlike most two-phase displacements the dispersion-free MMP may not exist for three-phase displacements, but rather a pressure is reached where the dispersion-free displacement efficiency is maximized. This is the first paper to examine a multiple mixing cell model where two- and three-hydrocarbon phases occur and to calculate the MMP and/or pressure required for high displacement efficiency for such systems.