Mixture models are commonly used in the simulation of transient two-phase flows as simplifications of six-equation models, with the drift-flux models as a common way to describe relative phase motion. This is particularly true in simulator and control system modeling where solutions that are faster than real time are necessary, and as a means for incorporating thermal-hydraulic feedback into steady-state and transient neutronics calculations. Variations on semi-implicit finite difference schemes are some of the more commonly used temporal discretization schemes. The maximum time-step size associated with these schemes is normally assumed to be limited by stability considerations to the material transport time across any computational cell (Courant limit). In applications requiring solutions that are faster than real time or the calculation of thermal-hydraulic feedback in reactor kinetics codes, time-step sizes that are restricted by the material Courant limit may result in prohibitive run times. A Courant violating scheme is examined for the mixture drift-flux equations, which for rapid transients is at least as fast as classic semi-implicit methods and for slow transients allows time-step sizes many times greater than the material Courant limit.