An absorbable, annealed surgical device made from a multi-phase, polymeric composition derived from lactide and glycolide. Preferably, the composition has two phases, both phases are continuous, the first phase has about 0-about 25%m glycolide moieties, the overall composition has up to 45%m glycolide moieties, and the first phase constitutes at least 50% (and preferably not more than about 95%) by weight of the composition. The device has a high distortion temperature, good resistance to hot-wet creep, but yet loses tensile strength in vivo quickly. The composition per se is injection-moldable, can be annealed, and is not brittle.