Catheter (100) having an elongated shaft (106) having an inner surface that defines a lumen (103) that extends distally from the proximal portion to an opening (118) at a distal terminus of a distal portion. In some embodiments the distal portion includes an inner polymer structure (114) having a first portion and a second portion positioned distal of the first portion along the length of the inner polymer structure. The first portion can have a first stiffness and the second portion can have a second stiffness less than the first stiffness. The distal portion can further include an outer polymer structure (116) disposed around the inner polymer structure and a coil (170) wound around the inner polymer structure and disposed within the outer polymer structure.
