A guidewire having a core member with proximal, intermediate and distal sections and a flexible coil on the distal section and a catheter assembly or kit with such guidewire. The proximal section of the core may be substantially longer than the combined lengths of both the intermediate and distal sections and has a diameter which is at least 0.001 inch greater than the diameter of the intermediate section. The intermediate section has a diameter which is at least 0.002 inch greater than the diameter of the distal section. Improved pushability and a greater flexibility in the distal and intermediate sections are obtained. A catheter which is used with the guidewire has a proximal section of about 100 cm and a distal section of at least about 15 cm in length and an inner lumen having diameter of at least 0.003 inch less than the inner diameter of the inner lumen in the proximal section.