An apparatus for providing percutaneous access to a vessel of a patient over a wire guide. An outer sleeve of the apparatus has proximal and distal open ends, and has a lumen extending longitudinally therethrough. An inner sleeve has proximal and distal open ends, and has a lumen extending longitudinally therethrough. The inner sleeve is sized to be received within the lumen of the outer sleeve. The inner sleeve has a main body portion having a distal portion that tapers toward its distal open end. The tapered distal portion extends distal to the distal open end of the outer sleeve to provide a generally smooth diametrical transition between the outer sleeve and the wire guide. A more rigid stiffening cannula has proximal and distal open ends, and has a lumen extending longitudinally therethrough. The lumen of the stiffening cannula is sized to receive the wire guide therethrough. The stiffening cannula is sized to be received within the lumen of the inner sleeve, and extends along the main body portion of the inner sleeve to a terminal point proximal to the inner sleeve distal end. The stiffening cannula and the inner sleeve are engaged such that relative axial movement between them is substantially inhibited. As a result, the inner sleeve distal portion acts as a shield for the distal end of the stiffening cannula distal end when the apparatus is percutaneously introduced into the vessel.