A guidewire includes a tapered core, an elongated non-radiopaque inner coil that is coincident with the core and extends over a distal portion of the core, and a radiopaque outer coil that fits over a distal end of the inner coil. The inner coil tapers between its proximal end and distal end, to form a tapered distal end section. The outer diameter of the proximal end of the inner coil is the same as the outer diameter of the proximal end of the core, before its first taper, and similarly, the outer diameter of the outer coil is the same as the outer diameter of the inner coil before its taper. Accordingly, the guidewire has an essentially uniform outer diameter over its entire length. A rounded tip that acts as a deformable buffer is formed where the distal ends of the two coils and the core join. The distal end of the core is preferably flattened to provide a formable end to the guidewire. A low friction coating may be added to the wire, to facilitate movement of the wire through the arteries.