The invention provides a rotational atherectomy device having, in various embodiments, a flexible, elongated, rotatable drive shaft with at least one flexible eccentric enlarged abrading head attached thereto. In other embodiments, the eccentric abrading head is not flexible or partially flexible. At least part of the eccentric enlarged cutting head has a tissue removing surface—typically an abrasive surface. In certain embodiments, the abrading head will be at least partially hollow. When placed within an artery against stenotic tissue and rotated at sufficiently high speeds the eccentric nature of the enlarged cutting head causes the cutting head and drive shaft to rotate in such a fashion as to open the stenotic lesion to a diameter substantially larger than the outer diameter of the enlarged cutting head. Preferably the eccentric enlarged cutting head has a center of mass spaced radially from the rotational axis of the drive shaft, facilitating the ability of the device to open the stenotic lesion to a diameter substantially larger than the outer diameter of the enlarged cutting head when operated at high speeds.