Poly(ester-carbonate) copolymers were synthesized through triethylborane (TEB)-activated, one-pot copolymerization of epoxides with anhydrides (AH) and CO2. Depending upon the feeding ratio of AH to the epoxides, poly(ester-carbonate) copolymers with random and tapered ester structures could be derived due to the much higher reactivity of AH toward growing oxanions compared to the reactivity of CO2. Anhydrides like succinic anhydride (SA) and phthalic anhydride (PA) when tried in terpolymerization with epoxides, like propylene oxide (PO) and cyclohexene oxide (CHO), and CO2 indeed exhibited such high reactivities in comparison to CO2 that tapered block structures were eventually obtained for high feeding ratios of AH to PO and random copolymers for the AH-to-epoxide feeding ratio lower than 10%. Terpolymerization with different feeding ratios of anhydrides to epoxides was thus systematically investigated. In an alternate path, diblock poly(ester-b-carbonate)s were prepared by sequential copolymerization of epoxide/anhydride and epoxide/CO2. All of the obtained copolymers were characterized by 1H nuclear magnetic resonance (NMR), diffusion-ordered spectroscopy (DOSY), gel permeation chromatography (GPC), and differential scanning calorimetry (DSC). The structures and properties of copolymers obtained by terpolymerizations and block copolymerizations were compared.