A method and apparatus for drilling glass using a drill and drill bit. The method utilizes a drill bit having a plurality of shaft diameters, and being provided with a plurality of types of abrasives. By providing a coarser abrasive on a narrow portion of the bit, and finer abrasives on a wider portion of the bit, drilling can be accomplished while reducing the incidents of micro fracture in the glass being drilled. Providing an even narrower connection shaft between the two cutting portions of the drill bit further facilitates reduction in micro fractures created during the drilling process.