A high-speed rotational atherectomy device for opening a stenosis in an artery having a given diameter, comprising: a guide wire having a maximum diameter less than the diameter of the artery; a flexible elongated, rotatable drive shaft advanceable over the guide wire, the drive shaft having a rotational axis; and at least one eccentric single piece unitary construction abrading head attached to the drive shaft, the eccentric abrading head comprising: a geometric center with a position that is radially offset from the rotational axis of the drive shaft; a center of mass with a position that is radially offset from the rotational axis of the drive shaft; wherein the positions of the geometric center and the center of mass are not coincident; proximal, intermediate and distal portions (30, 35, 40), wherein the proximal portion comprises a proximal outer surface and a length, the intermediate portion comprises an intermediate outer surface and the distal portion comprises a distal outer surface and a length, the proximal outer surface having diameters that increase distally and a proximal radiused edge, the distal outer surface having diameters that decrease distally and a distal radiused edge, and the intermediate outer surface being cylindrical; wherein at least the intermediate outer surface comprises tissue removal sections; wherein the abrading head defines a drive shaft lumen therethrough and a hollow chamber having a size and a shape, the drive shaft at least partially traversing the drive shaft lumen; wherein the abrading head is formed from a material having a density in the range of 8-22.5 g/cm 3; and wherein the radial offset of the center of mass of the abrading head from the rotational axis of the drive shaft is affected by the density of the material forming the abrading head, the lengths of the proximal and distal portions (30, 40) and the size and shape of the hollow chamber. a guide wire having a maximum diameter less than the diameter of the artery; a flexible elongated, rotatable drive shaft advanceable over the guide wire, the drive shaft having a rotational axis; and at least one eccentric single piece unitary construction abrading head attached to the drive shaft, the eccentric abrading head comprising: a geometric center with a position that is radially offset from the rotational axis of the drive shaft; a center of mass with a position that is radially offset from the rotational axis of the drive shaft; wherein the positions of the geometric center and the center of mass are not coincident; proximal, intermediate and distal portions (30, 35, 40), wherein the proximal portion comprises a proximal outer surface and a length, the intermediate portion comprises an intermediate outer surface and the distal portion comprises a distal outer surface and a length, the proximal outer surface having diameters that increase distally and a proximal radiused edge, the distal outer surface having diameters that decrease distally and a distal radiused edge, and the intermediate outer surface being cylindrical; a geometric center with a position that is radially offset from the rotational axis of the drive shaft; a center of mass with a position that is radially offset from the rotational axis of the drive shaft; wherein the positions of the geometric center and the center of mass are not coincident; proximal, intermediate and distal portions (30, 35, 40), wherein the proximal portion comprises a proximal outer surface and a length, the intermediate portion comprises an intermediate outer surface and the distal portion comprises a distal outer surface and a length, the proximal outer surface having diameters that increase distally and a proximal radiused edge, the distal outer surface having diameters that decrease distally and a distal radiused edge, and the intermediate outer surface being cylindrical; wherein at least the intermediate outer surface comprises tissue removal sections; wherein the abrading head defines a drive shaft lumen therethrough and a hollow chamber having a size and a shape, the drive shaft at least partially traversing the drive shaft lumen; wherein the abrading head is formed from a material having a density in the range of 8-22.5 g/cm 3; and wherein the radial offset of the center of mass of the abrading head from the rotational axis of the drive shaft is affected by the density of the material forming the abrading head, the lengths of the proximal and distal portions (30, 40) and the size and shape of the hollow chamber.