Improved medical filaments for use with dilators to be inserted into a patient, for example into the vascular lumen, are provided, as well as combinations of filaments and dilators. Methods for use of such filaments and filament-dilator combinations are also described. The filament includes a proximal segment and a distal segment. The diameter of the distal segment is greater than the diameter of the proximal segment. The change in diameter is abrupt, providing a discrete step transition at a point along the filament which presents a proximally-facing surface on the distal segment. When the proximal segment of the filament is fully inserted into a dilator having a distal tip adapted for insertion into a patient, the dilator distal tip firmly abuts the proximally-facing end surface of the distal segment. The relative dimensions of the dilator tip and the discrete stepped transition of the filament provides full shielding or over shielding of the dilator tip, thereby facilitating passage of the dilator tip along the tissue track, through the puncture hole and into the orifice.