A catheter comprising an elongate tubular member having a proximal end, a distal end, and a passageway defining a lumen extending between the proximal and distal ends. The elongate tubular member comprises a relatively stiff proximal section and a relatively flexible distal section. The proximal section includes an inner tubular liner, a first stiffener comprising a metal alloy, and a second stiffener comprising a non-metal alloy. The first and second stiffeners are coaxially wound exterior to the proximal inner liner. The distal section includes a distal inner tubular liner and the second stiffener coaxially wound exterior to the distal inner liner. The first stiffener terminates before reaching the distal section.