The important role that the order-disorder transition temperature (T-ODT) of a block copolymer plays in the compatibilization of two immiscible homopolymers is demonstrated, using the model ternary blend systems consisting of a polystrene-block-polybutadiene (SB diblock) copolymer and two immiscible homopolymers, polystyrene (hPS) and polyisoprene (hPI). For the study, SB diblock copolymers hating different microstructures were employed. We investigated via transmission electron microscopy (TEM) the morphology of the blends. We found that an SB diblock copolymer was very poorly distributed at the inter face between hPS and hPI in an hPS/hPI/SB ternary blend when the specimen was annealed at a temperature below the T-ODT of the block copolymer, while a more uniform distribution of the SB diblock copolymer was observed when a specimen was annealed at a temperature above its T-ODT. We have shown that the miscibility (or the interaction parameter) between the hPI and PB block in an SB diblock copolymer plays a decisive role in controlling the morphology at the interfaces between hPS and hPI. We conclude that a block copolymer must be designed, such that its T-ODT is below the targeted melt blending temperature, in order for the block copolymer to be able to act as an effective compatibilizing agent for two immiscible homopolymers. This conclusion is supported further by investigating the tensile properties and morphology of ternary blends consisting of polypropylene (PP), hPS, and polystyrene-block-poly(ethylene-co-1-butene)-block-polystyrene (SEBS triblock) copolymer (Kraton G1650), which were prepared by melt blending at 200 degrees C in a batch mixer. That is, little improvement in the tensile properties of the ternary blends was observed when Kraton G1650 was added to PP/hPS binary blends. This observation is explained by a very poor distribution, observed by TEM, of Kraton G1650 at the interface between PP and hPS in the ternary blend, This is attributed to the very high T-ODT, estimated to be above 350 degrees C from currently held mean-field theory, of Kraton G1650 compared to the melt blending temperature employed.