Methods for making bioabsorbable copolymer filaments are provided herein. The methods include drying the polymer pellets to be extruded, melt extrusion of copolymer components, stretching the filaments in one or more draw steps and permitting the drawn filaments to relax. The copolymer preferably contains units derived from glycolide or glycolic acid and units derived from an alkylene carbonate, such as, for example, trimethylene carbonate.