Methods to produce structures containing ultrafine fibers with average diameters from 10 nm to 10 &mum and more preferably from 50 nm to 5 &mum, have been developed. These methods produce ultrafine fibers without substantial loss of the polymers weight average molecular weight. The ultrafine electrospun fibers have an unexpectedly higher degree of molecular orientation, and higher melt temperature than fibers derived by dry spinning. In the preferred embodiment, the polymer comprises 4-hydroxybutyrate. The ultrafine fibers are preferably derived by electrospinning. A solution of the polymer is dissolved in a solvent, pumped through a spinneret, subjected to an electric field, and ultrafine fibers with a high degree of molecular orientation are collected. These structures of ultrafine fibers can be used for a variety of purposes including fabrication of medical devices.