We investigate the compatibilizing performance of a random copolymer in the melt state, using transmission electron microscopy. Blends of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are chosen as a model system, and a random copolymer of styrene and methyl methacrylate (SMMA) with 70 wt % styrene is used as a compatibilizer. From TEM photographs it is clear that SMMA moves to the interface between PS and PMMA domains during melt mixing, and forms encapsulating layers. However, the characteristic size of the dispersed phase increases gradually with annealing time for all blend systems studied. This demonstrates that the encapsulating layer of SMMA does not provide stability against static coalescence, which calls into question the effectiveness of random copolymers as practical compatibilizers. We interpret the encapsulation by random copolymers in terms of a simple model for ternary polymer blends.