Copolymers having repeating units derived from monocyclic esters or carbonates and certain bicyclic diesters and/or carbonates have controllable rheological properties. The bicyclic diester and/or carbonate copolymerizes easily with the monocyclic monomers, especially with lactide, to form copolymer that can have tailored levels of branching. The copolymers have excellent rheological properties, including increased melt tensions and improved shear thinning, compared to the analogous linear polymers.