A method of making a stent comprises the steps of: (a) dip-coating (230) a mandrel (210) in a solution (220) comprising one or more biocompatible polymers to form a polymer tube; (b) spin-drying (240) the polymer tube around its longitudinal axis; (c) solvent-polishing (250) and vacuum drying the polymer tube; and, (d) necking (260) the polymer tube by drawing the mandrel bearing the polymer tube through one or more necking dies of decreasing diameter, wherein said necking is carried out at a temperature above the glass transition temperature of the polymer and below the melting temperature of the polymer.