An introducer apparatus includes an outer sleeve and an inner cannula received within the lumen of the outer sleeve. The outer sleeve has a profile such that at least a portion of the distal end of the outer sleeve tapers in the distal direction at an angle not exceeding about 2° relative to a longitudinal axis of the apparatus. The distal open end of the outer sleeve has a wall thickness not exceeding about 0.003 inch. The inner cannula includes a tapered distal end portion. The tapered distal portion of the inner cannula extends distal to the distal open end of the outer sleeve, such that a generally smooth diametrical transition is provided between the outer sleeve tapered portion and the open distal end of the inner cannula.
