Novel catheter constructions comprising thin covering or wrapping materials such as polymer films. A catheter provided with a guidewire catheter lumen having a thin covering that is easily punctured by a guidewire at virtually any desired point along the catheter length. The thin covering may be integral with the catheter shaft, or may be a separate component that covers only the portion of the catheter shaft immediately adjacent the outer portion of the guidewire lumen, or may be a thin tubular construct that surrounds the entire catheter shaft. Moreover, polymer film can be used in combination with one or more elements to produce novel catheter constructions.