A method is presented for dispersing ropes or bundles of single-walled carbon nanotubes (RCNTs) in a polycarbonate (PC) matrix. Films of PC/RCNT composites are produced, with thicknesses ranging from 10 to 60 mum, and containing small concentrations (0.06-0.25 wt.-%) of RCNT. Our process is based on a unique method of hot casting, annealing, and drying from dichlorobenzene solution. A wet annealing prior to complete drying yields a uniform and transparent film. Despite the low RCNT loading, scanning electron microscopy (SEM) analysis of the films after fracture reveals that the RCNTs form an entangled network throughout the film, which is a key requirement for enhanced properties. An increase of up to 30% in the Young's modulus, as compared to PC, results with this method of composite fabrication.