This is directed to a cable structure for use with an electronic device. The cable structure can include one or more conductors around which a sheath is provided. To prevent the cable structure from tangling, the cable structure can include a core placed between the conductors and the sheath, where a stiffness of the core can be varied along different segments of the cable structure to facilitate or hinder bending of the cable structure in different areas. The size and distribution of the stiffer portions can be selected to prevent the cable from forming loops. The resistance of the core to bending can be varied using different approaches including, for example, by varying the materials used in the core, varying a cross-section of portions of the core, or combinations of these.