Minimum miscibility pressure (MMP) is one of the most important parameters in the design of successful gas floods. One technique for calculation of MMP uses the analytical method based on the method of characteristics (MOC). Although MOC is the fastest MMP calculation method available today, it can suffer from robustness owing to complex phase behavior observed in some field displacements. The current MOC method implemented in commercial software assumes that the composition route is composed of a series of shocks from one key tie line to the next. For some displacements, however, these key tie lines do not control miscibility and significant errors in MMP can result. One way to eliminate the error lies in constructing the entire composition route, which is challenging for many complex multicomponent oil displacements. This paper examines how to determine the unique composition route for all conceivable phase behavior complexities, making the MOC method for MMP calculation significantly more robust. The approach relies on solving for all tie lines in the composition route directly, independent of fractional flow. MMP estimation is based solely on the tie-line route calculation in tie-line space, where both tie-line rarefactions and shocks may exist. MMPs that result from 1-D displacements of oil by gas are therefore decoupled from fractional flow, making the calculation significantly easier and more robust. Once tie lines in the composition route are determined, specific compositions for a given fractional flow can be mapped onto the tie-line solution, completing the composition route if desired. Compared to current methods, the formulation in tie-line space has a smaller rank, few or no umbilic points, and as stated is independent of fractional flow. Example solutions show that MMPs are easily calculated with this approach for complex displacements that were incorrectly or very difficult to solve before, including multicomponent gas injection with bifurcating phase behavior.