A method is proposed for reproducing early gas breakthrough when performing full-field compositional simulation of gas injection in under-saturated oil. It was developed by solving the successive problems encountered on a real heterogeneous field with a gas injection pilotThe first problem was to correctly model transport in this large carbonate field using a coarse grid. It was dealt with by using alpha-factors. The second difficulty was related to the strong under-saturation of the oil: all injected gas dissolves until saturation pressure reaches actual block pressure. In practice, this means that gas will appear too late in the simulation. This is easily avoidable in black-oil simulation, but compositional simulators will usually not allow to circumvent the equation of state. We found out that correcting the critical transition allowed to speed up the appearance of the gas phase. A third difficulty was to history match the gas injection pilot without distorting the geological model. We thus wanted to reproduce the inherent instability of gas injection, which had not swept all layers homogeneously, as shown by time-lapse RST data. This problem was solved using an extra-capability of alpha-factors: stating that the transported fluid viscosity is lower than average grid-block viscosity, and integrating this new correction into the oil and gas alpha-factor table, allowed to successfully reproduce quick gas encroachment in permeable layers. The fourth task of imposing a residual oil saturation Sorm was solved using the end-point of the alphafactor table.Thus we propose a method for correcting several effects simultaneously: acceleration of the light components, acceleration of the critical transition from volatile oil to gas condensate, viscosity correction to reproduce gas fingering, and slow-down of the heavy components in order to force residual oil saturation. To our knowledge, documentation of the second and third corrections is new. All four corrections being justified, we used them all in a composite alpha-factor table.