A self-centering atherectomy device configured with a distal portion having a gradually increasing diameter in the proximal direction for opening a chronic total occlusion within a blood vessel being characterized by complete interruption of blood flow, said distal portion comprising: a rotatably motor-driven flexible hollow shaft that is slidable over a guidewire and is coaxial with a longitudinal axis of the guidewire; an annular distal tip of the hollow shaft having a first diameter that is only slightly larger than the diameter of the guidewire and configured with cutting surfaces defining said first diameter for piercing plaque that has accumulated within a blood vessel; a tubular sleeve proximally spaced from said distal tip of the hollow shaft, and fitted over, and secured to, a first peripheral surface of the hollow shaft, wherein a distal end of said sleeve has a second diameter which is slightly larger than said distal tip of the hollow shaft and is configured with cutting surfaces for enlarging an opening formed in the plaque; and a cutting unit defining a third diameter larger than said sleeve for additionally enlarging said opening, wherein the cutting surfaces of said distal tip are distal to said sleeve and are circumferentially extending, and are adapted to pierce hardened atherosclerotic plaque of a chronic total occlusion characterized in that said cutting unit is an asymmetric cutting unit extending between said sleeve and a second peripheral surface of the hollow shaft which is proximally spaced from said first peripheral surface and having a radial separation from said hollow shaft at one longitudinally central region of said cutting unit that is significantly greater than the radial separation from said hollow shaft at other longitudinal regions of said cutting unit, wherein said cutting unit is configured to ensure atraumatic contact with a wall of the blood vessel during lateral movement of the atherectomy device, wherein the asymmetric cutting unit facilitates eccentric rotation of the hollow shaft about the longitudinal axis to result in lateral displacement in a first direction within the blood vessel and subsequently in a second direction opposite to said first direction in response to atraumatic impact between said cutting unit and the wall of the blood vessel, so as to be substantially self-centered within the blood vessel as a result of alternating lateral movement, wherein the cutting surfaces of said distal tip, following a self-centering action, are configured to pierce a central relatively soft plaque region of the chronic total occlusion, and the cutting surfaces of said sleeve and of said cutting unit are configured to sequentially enlarge the opening while said distal tip remains in engagement with said central region. a rotatably motor-driven flexible hollow shaft that is slidable over a guidewire and is coaxial with a longitudinal axis of the guidewire; an annular distal tip of the hollow shaft having a first diameter that is only slightly larger than the diameter of the guidewire and configured with cutting surfaces defining said first diameter for piercing plaque that has accumulated within a blood vessel; a tubular sleeve proximally spaced from said distal tip of the hollow shaft, and fitted over, and secured to, a first peripheral surface of the hollow shaft, wherein a distal end of said sleeve has a second diameter which is slightly larger than said distal tip of the hollow shaft and is configured with cutting surfaces for enlarging an opening formed in the plaque; and a cutting unit defining a third diameter larger than said sleeve for additionally enlarging said opening, wherein the cutting surfaces of said distal tip are distal to said sleeve and are circumferentially extending, and are adapted to pierce hardened atherosclerotic plaque of a chronic total occlusion characterized in that said cutting unit is an asymmetric cutting unit extending between said sleeve and a second peripheral surface of the hollow shaft which is proximally spaced from said first peripheral surface and having a radial separation from said hollow shaft at one longitudinally central region of said cutting unit that is significantly greater than the radial separation from said hollow shaft at other longitudinal regions of said cutting unit, wherein said cutting unit is configured to ensure atraumatic contact with a wall of the blood vessel during lateral movement of the atherectomy device, wherein the asymmetric cutting unit facilitates eccentric rotation of the hollow shaft about the longitudinal axis to result in lateral displacement in a first direction within the blood vessel and subsequently in a second direction opposite to said first direction in response to atraumatic impact between said cutting unit and the wall of the blood vessel, so as to be substantially self-centered within the blood vessel as a result of alternating lateral movement, wherein the cutting surfaces of said distal tip, following a self-centering action, are configured to pierce a central relatively soft plaque region of the chronic total occlusion, and the cutting surfaces of said sleeve and of said cutting unit are configured to sequentially enlarge the opening while said distal tip remains in engagement with said central region.