Abstract: A guidewire for medical use such as in vascular and nonvascular systems. The guidewire made from a titanium molybdenum alloy wire with a composition of approximately 78% titanium 11.5% molybdenum 6% zinc and 4.5% tin by weight such that it is softer than stainless steel guidewires and stiffer than NiTi alloy guidewires. The distal end of the guidewire is of a smaller diameter and softer than the proximal end and fitted with a coil for springiness such that the distal end will bend when encountering curves in the body passageways. The distal tip may be heat treated for a gradient of softness with the distal tip being the softest. The distal end may also be tapered to provide an additional gradient of softness. A distal tip on the distal end of the guidewire protects the wall of the passageway from being punctured as the guidewire travels through the passageway.