Rapid exchange angioplasty catheters and methods of constructing rapid exchange angioplasty catheters including features that provide good pushability and kink resistance. In an illustrative embodiment, a catheter is provided, the illustrative catheter including a proximal hypotube section, which connects to a more distal braided catheter section. The braided catheter section connects to a midshaft portion that includes a guidewire entry port. Distal of the midshaft portion is a distal section having a balloon disposed thereon. An inflation lumen extends the length of the catheter, while a guidewire lumen extends only from the guidewire entry port to the distal end of the catheter. Optionally, a core wire may extend across the joint from the hypotube, to the braided catheter section, and past the guidewire entry port.