An angioplasty guidewire includes a proximal shaft formed with an axial passage and a variable stiffness intermediate section extending axially from the tubular shaft and having a corridor aligned axially with the passage and terminating at a distal joint. The intermediate section comprises a plurality of stiffening elements. A core element is slidably disposed axially through the passage and includes a distal end projecting into the corridor and attached to the distal joint while a flexible distal tip is mounted to the end of the intermediate portion and projects axially therefrom.