Absorbable polyester fibers, braids, and surgical meshes with improved handling properties have been developed. These devices are preferably derived from biocompatible copolymers or homopolymers of 4-hydroxybutyrate. These devices provide a wider range of in vivo strength retention properties than are currently available and have a decreased tendency to curl, in the preferred embodiment, due to the inclusion of relaxation and annealing steps following methods are characterized by the following physical properties: (i) elongation to break from about 17% to about 85% (ii) Young's modulus of less than 350,000 psi, (iii) knot to straight ratio (knot strength/tensile strength) of 55-80% or (iv) load at break from 1100 to 4200 grams.