Tubular devices are provided that include a proximal end, a distal end sized for introduction into a patient's body, a central lumen, a conductor extending between the proximal and distal ends adjacent the central lumen, reinforcement members including windings extending helically around the central lumen, and an outer jacket. The tubular device includes a first portion in which the conductor extends helically around the central lumen, and a second portion in which the conductor extends longitudinally and either a) all of the windings surround the central lumen and the conductor remains outside the windings, b) at least some of the windings pass between the central lumen and the conductor and at least some of the windings surround both the central lumen and the conductor, and c) all of the windings surround both the central lumen and the conductor. Methods for making such tubular devices are also provided.