The phase behavior of branched polycarbonate (BPC) blends with poly(ethylene terephthalate-co-1,4-dimethyl cyclohexane terephthalate) copolyesters (PECT), as well as their rheological properties, were assessed. Even though BPC blends with PECT prepared by solvent casting proved to be immiscible, BPC and PECT copolyesters containing 1,4-dimethyl cyclohexane (CHDM) from 32 to 80 mole% formed homogeneous mixtures upon heating. The homogenization temperatures of the blends decreased with increasing CHDM content in PECT. The interaction energies of the BPC-PECT pairs calculated from the phase boundary in accordance with the lattice-fluid theory were positive and also decreased with increasing CHDM content in PECT. It was shown that the phase homogenization of these blends occurs upon heating when the combinatorial entropy term, which is favorable for miscibility, overcomes unfavorable energetic terms at elevated temperatures. A novel product, which is not limited by the drawbacks of linear polycarbonate (PC) and evidences processability superior to that of the PC/PECT blends, can be developed via the blending of BPC and PECT.