A first guidewire structure includes a medical guidewire having a working portion which is extendable beyond a distal end of a medical instrument. The working portion has a length, and the working portion is tapered for substantially one-hundred percent of the length. A second guidewire structure includes a medical guidewire having a working portion, wherein the working portion has a length, and wherein the working portion includes a tapered portion for over fifty percent of the length. A third guidewire structure includes a medical guidewire having a working portion. The working portion has a length, and the working portion includes a plurality of lengthwise-adjoining segment pairs for over fifty percent of the length. Each segment pair consists essentially of a non-tapered segment having a substantially constant cross section and a tapered segment lengthwise adjoining the non-tapered segment. Methods are described for using medical instruments having the guidewire structures.
