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 extrusion and orientation of the fiber. Filaments prepared according to these 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.