Continuous processing methods for making absorbable polymeric dry spun non-wovens with one or more of the following properties: high burst strength, fine fibers of average diameter from 0.01 µm to 50 µm, and thickness from 10 µm to 10 mm, have been developed. Improved fiber cohesion is made possible by controlling the tackiness of the fibers of the non-woven during web collection. The polymer is preferably a polyhydroxyalkanoate, more preferably, a 4-hydroxybutyrate polymer or copolymer. A non-woven of poly-4-hydroxybutyrate is most preferred. The non-wovens have fine fibers with average diameters ranging from 0.01µm to 50 µm, and are derived by dry spun processing, during which a solution of polymer(s) is injected into a stream of high velocity air with a pressure of 1 to 500 psi for solvent stripping and polymer strand attenuation. The non-wovens can be used for a variety of purposes including fabrication of medical devices.