The invention is directed to a guidewire having a distal section with multiple distally tapered core segments with at least two contiguous distally tapering core segments in which the most distal tapered core segment preferably has a greater degree of taper than the proximally contiguous tapered core segment. The invention is also directed to an elongated intracorporeal device, preferably a guidewire or section thereof, that has a core member with a plurality of contiguous tapered segments having taper angles that are configured to produce a linear change in stiffness over a longitudinal section of the device. The device may also have a core section with a continuously changing taper angle to produce a curvilinear profile that preferably is configured to produce a linear change in stiffness of the core over a longitudinal section of the device.