Catheters adapted for use in small body vessels are described. A catheter (10, 110, 210, 210', 210") includes an elongate shaft (12, 112, 212, 212', 212") having a main body (30, 130, 230, 230', 230") that defines first (34, 134, 234, 234', 234") and second (38, 138, 238, 238', 238") lumens. An inner tubular member (40, 140, 240, 240', 240") is disposed in the second lumen and is formed of a material that has a stiffness that is greater than a stiffness of the material forming the main body and that has an elastic modulus greater than or equal to about 400 MPa.
