In mixing of immiscible fluids, the final steady state drop size distribution, corresponding to a minimum mean drop size, is commonly approached in a monotonic way. There are, however, other scenarios. Overemulsification refers to cases where, (I) after reaching a minimum, the average size increases and then levels off to a final size, or (II) the average size oscillates. In case (I) the drop size distribution becomes bimodal after the average size goes through a minimum; gradually, the peak at smaller sizes moves towards the peak at larger sizes resulting in a narrow distribution, An explanation of this phenomenon is offered and ways to exploit it are suggested.