A composite wire, such as a guide wire, may include a principal section with a relatively large outer diameter, as well as one or more reduced sections with smaller outer diameters. The relatively small outer diameter of each reduced section may be defined by an inner element of the composite wire, while the relatively large outer diameter of the principal section may be defined by one or more outer elements that reside on, and may surround, the inner element. The inner and outer elements may be formed from materials that impart the composite wire with one or more desired characteristics, such as a stiffness, hardness and flexibility. In specific embodiments, the inner element may comprise a standard, small diameter guide wire, while the outer element comprises a tube formed from polyether ether ketone (PEEK). Each outer element may be secured to the inner element at one or more locations. Differences in characteristics between locations where the outer element has been coupled to the inner element and locations where the outer element merely resides on the inner element may be used to tailor characteristics of the composite wire.