A vascular guidewire introducer device (10) having a needle (52), a bulb (16), and a valve subassembly (100) through which a guidewire (14) is insertable for vascular guidewire insertion into a blood vessel (12) of a patient. The valve subassembly (100) includes a proximal fitting (102), a proximal cap (106), and a valve arrangement (104) disposed within a valve seat (118) defined by one of the fitting and the cap. The valve arrangement includes distal and proximal disc-shaped valve members (122,126) having centered slits (124,128) therethrough, and a spacer (130) disposed between the valve members. A method is disclosed for precisely centering the slits of the valve members during assembly and for retaining the valve members in their precisely centered positions in the valve seat. The valve arrangement permits use with a wide range of guidewire diameters.