CO2 flooding at low temperatures often results in three or more hydrocarbon-phases. Multiphase compositional simulation must accurately simulate such gas floods. Drawbacks of modeling three hydrocarbon-phases are the increased computational time and convergence problems associated with flash calculations. Use of a reduced method is a potential solution. We first demonstrate the importance of using three-phase flash calculations in compositional simulation by investigating difficulties with two-phase equilibrium approximations proposed in the literature. We then extend an algorithm for reduced two-phase flash calculations to three-phase calculations and show the efficiency and robustness of our algorithm. The reduced three-phase flash algorithm is implemented in a multiphase compositional simulator to demonstrate the speed-up and increased robustness of simulations in various case studies. Results show that use of a two-phase equilibrium approximation in reservoir simulation can result in a complete failure or erroneous simulation results. Simulation case studies show that our reduced method can significantly decrease computational time without loss of accuracy. Computational time is reduced because of the smaller number of equations to be solved and increased time-step sizes. We show that phase behavior convergence problems lead directly to reduced time-step sizes.