A process for producing a coated filter plug for a smoking article including: (a) incorporating an additive to a porous filter plug, thereby obtaining an impregnated filter plug; (b) coating a surface of the impregnated filter plug with a cross-linkable polymer material; and (c) cross-linking the cross-linkable polymer material, to form a cross-linked, breakable coating substantially enclosing the impregnated filter plug. The process may further include at least partially coating the impregnated filter plug with a cross-linking agent prior to, or subsequent to, coating with the cross-linkable polymer material.