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; and a flexible elongated, rotatable drive shaft advanceable over the guide wire, the drive shaft having a rotational axis; an eccentric abrading head attached to the drive shaft, characterized by the abrading head comprising: an eccentric proximal segment defining a drive shaft lumen therethrough, wherein the proximal segment is mounted on the drive shaft; at least one eccentric cylindrical segment separate from the eccentric proximal segment, the at least one eccentric cylindrical segment defining a drive shaft lumen therethrough, wherein the at least one eccentric cylindrical segment is mounted distally and separately from the eccentric proximal segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the proximal segment are spaced apart along the drive shaft by a first flexibility gap; and an eccentric distal segment separate from the at least one eccentric cylindrical segment, the eccentric distal segment defining a drive shaft lumen therethrough, wherein the eccentric distal segment is mounted distally and separately from the at least one eccentric cylindrical segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the eccentric distal segment are spaced apart along the drive shaft by a second flexibility gap. a guide wire having a maximum diameter less than the diameter of the artery; and a flexible elongated, rotatable drive shaft advanceable over the guide wire, the drive shaft having a rotational axis; an eccentric abrading head attached to the drive shaft, characterized by the abrading head comprising: an eccentric proximal segment defining a drive shaft lumen therethrough, wherein the proximal segment is mounted on the drive shaft; at least one eccentric cylindrical segment separate from the eccentric proximal segment, the at least one eccentric cylindrical segment defining a drive shaft lumen therethrough, wherein the at least one eccentric cylindrical segment is mounted distally and separately from the eccentric proximal segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the proximal segment are spaced apart along the drive shaft by a first flexibility gap; and an eccentric distal segment separate from the at least one eccentric cylindrical segment, the eccentric distal segment defining a drive shaft lumen therethrough, wherein the eccentric distal segment is mounted distally and separately from the at least one eccentric cylindrical segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the eccentric distal segment are spaced apart along the drive shaft by a second flexibility gap. an eccentric proximal segment defining a drive shaft lumen therethrough, wherein the proximal segment is mounted on the drive shaft; at least one eccentric cylindrical segment separate from the eccentric proximal segment, the at least one eccentric cylindrical segment defining a drive shaft lumen therethrough, wherein the at least one eccentric cylindrical segment is mounted distally and separately from the eccentric proximal segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the proximal segment are spaced apart along the drive shaft by a first flexibility gap; and an eccentric distal segment separate from the at least one eccentric cylindrical segment, the eccentric distal segment defining a drive shaft lumen therethrough, wherein the eccentric distal segment is mounted distally and separately from the at least one eccentric cylindrical segment on the drive shaft, wherein the at least one eccentric cylindrical segment and the eccentric distal segment are spaced apart along the drive shaft by a second flexibility gap.