Alcohol-initiated ring-opening alternating copolymerization (ROAP) of phthalic anhydride (PA) and a variety of mono-, di-, and trisubstituted epoxides has been performed with a weak phosphazene base (t-BuP1) as the catalyst. Each product exhibits a perfectly alternating sequence distribution, controlled molar mass (M-n up to 124 kg mol(-1), and low dispersity (D-M < 1.15, mostly). Full conversion of PA can be reached in 0.5-24 h depending on the substituent of the epoxide, the targeted degree of polymerization, and the amount of t-BuPi used (0.2-5 mol % of PA) when the reactions are conducted under solvent-free conditions at 100 degrees C with a small excess of the epoxide (0.5 equiv of PA). The glass transition temperature of the polyester ranges from -14 to 135 degrees C. The living nature of the ROAP allows one-pot construction of well-defined block-alternating copolymers through sequential addition of two epoxides. Statistical-alternating copolymers have also been synthesized by copolymerization of PA and two mixed epoxides. Thus, the structural diversity of aromatic alternating polyesters synthesized by this simple organocatalysis has been largely enriched.