catheter devices having low profile shafts and laterally deployable members that may be extended or advanced laterally from the catheter shaft . also disclosed are methods for bypassing a vascular obstruction wherein a guidewire is entrapped in a subintimal space adjacent to the obstruction . a catheter of the foregoing character is advanced over the entrapped guidewire and into the subintimal space . the laterally deployable member is then advanced or extended from the subintimal space back into the true lumen of the blood vessel distal to the obstruction . a second guidewire is then advanced through or along the laterally deployable member . the catheter and first guidewire are then removed and one or more working device is / are advanced over the second guidewire and used to establish a subintimal bypass channel through which blood may flow around the obstruction .