A medical introducer includes an elongated tubular member having a proximal end, a distal portion, and a central lumen extending from the proximal end to a distal port in the distal portion. A frame structure is coupled to the distal portion of the elongated tubular member, where frame structure supports the distal portion of the elongated tubular member in a tapered shape and alternatively in a non-tapered shape. The elongated tubular member may include a rigid outer tube and a rigid inner tube carried in an interior lumen of the outer tube. The distal portion is typically a reinforced elastomeric tubular extension of the outer tube, and the reinforced elastomeric tubular extension may have a conical shape.