A guidewire or section thereof, that has a core member or the like with a plurality of contiguous tapered segments having taper angles that are configured to produce a linear change in stiffness over a longitudinal portion of the device. The device may also have a core section with a continuously changing taper angle to produce a curvilinear profile that is configured to produce a linear change in stiffness of the core over a longitudinal portion of the device. An embodiment has a plurality of radiopaque elements that may be intermittent, continuous or in the form of a helical ribbon for scaled measurement of intracorporeal structure under fluoroscopic imaging. Another embodiment has at least one layer of polymer over the distal end of the device.