A medical catheter for inserting into a body includes a bump tubing section with proximal and distal ends, wherein the proximal end is configured to mate with a hub. The bump tubing section has an intermediate portion extending away from the proximal end with a substantially constant outer diameter and thickness, and a taper portion adjacent the distal end with generally decreasing inside and outside diameters to provide a gradually increasing flexibility toward the distal end of the bump tubing section. The bump tubing section is comprised of a polymer having a predetermined flexural modulus. A tip section is disposed distally of the distal end of the bump tubing section comprising a distal liner and a distal cover such that at least a majority of the tip section has a substantially constant stiffness and a flexural modulus substantially equal to or greater than the predetermined flexural modulus.
