Quantitative measurements of the effect of a third phase of buoyant solid particles on the settling rates of suspensions of heavy particles are reported. It is found that for a wide range of concentration of both buoyant and heavy particles, the settling rates of both solid phases are greatly increased. If the phases are dilute, the settling velocities of both are retarded. The total settling time of heavy particles can be halved, but only under conditions that the light phase is unaccelerated. This suggests that small gas bubbles would form a more satisfactory buoyant phase. The high concentrations of thickened suspensions which result from the acceleration process are also reported.