Blends of anionically-polymerized polybutadiene (BR) and styrene-butadiene copolymer (SBR) must be treated as mixtures of terpolymers and tetrapolymers, due to the presence of three different BR isomers : cis-1,4, trans-1,4, and vinyl-1,2. Moreover, in the absence of specific interactions or chemical reactions that strongly influence miscibility, structural characteristics of the component polymers, such as BR isomer content, SBR styrene content, monomer sequence distribution, molecular weight, and molecular weight distribution, are expected to have an increased role in determining the blend miscibility characteristics. Small angle neutron scattering (SANS) studies of SBR/BR blends have resulted in the computation of the monomer-monomer segmental interaction energetics via a Flory-Huggins treatment. This allows quantitative prediction of miscibility behavior as a function of polymer structure. We have used the Flory-Huggins chi parameters, describing the styrene/cis-1,4, styrene/trans-1,4, and cis-1,4/trans-1,4 segmental interactions, to identify certain blend combinations expected to exhibit phase transitions in an experimentally accessible temperature range. The appropriate polymers were synthesized, solution blended, and the blends analyzed via optical microscopy and thermal analysis. Our results show that the blend behavior, observed experimentally, is consistent with the calculated cloud point curves.