Apparatus and method for performing an atherectomy. The apparatus includes a rotational atherectomy device having a flexible, elongated drive shaft and an abrasive burr carried on the drive shaft. The drive shaft and abrasive burr each include a central lumen so that they can be advanced over a guide wire. The apparatus further includes a guide wire having a generally straight proximal portion, a flexible distal end portion, and an intermediate, flexible burr positioning segment. The burr positioning segment includes a predetermined curved shape so that when the abrasive burr is advanced over the guide wire to a position along the curved burr positioning segment, the burr positioning segment positions the burr laterally away from the axes of the proximal and distal portions of the guide wire, thus giving control over the lateral position of the burr within an artery. The device therefore allows selective removal of tissue from one side of an artery, permitting selective treatment of eccentric lesions without damaging the artery wall, and permitting treatment of lesions generally without blocking blood flow during use.