Bicomponent fibers comprising a core of a thermoplastic material, preferably polypropylene, and a sheath of a blend of the core-forming polymer and an ethylene-vinyl acetate copolymer are used to produce tobacco smoke filter elements which may be incorporated into tobacco smoke filter products such as filtered cigarettes. The addition of significant quantities of the core-forming material to the ethylene-vinyl acetate used to form the sheath avoids problems experienced heretofore in build-up of polymer in the forming dies using conventional filter-forming equipment. Additionally, the blended sheath-forming polymer improves adhesion between the sheath and the core of the bicomponent fiber and, with the use of polypropylene, improves the hardness of the resultant tobacco smoke filter elements.