A dental surgery apparatus comprises a drill 101 and a plurality of attachable sleeves (201, 702, 802). The drill has a shaft 102 comprising a working portion 104 and a fitting portion 105 which engages with a dental handpiece 106 and being provided with a positioning collar 109. Each sleeve (201, Fig 2) has a body (202, Fig 2) defining a passageway therethrough allowing the sleeve and drill to be assembled such that the sleeve and drill are rotatable about a common axis of rotation (302, Fig 3). The passageway of each sleeve is provided with an internal abutment flange which co-operates with the positioning collar to define a relative position of the sleeve along the drill. The body is also provided with a sleeve shoulder (205, Fig 2) between an insertion portion (206, Fig 2) and an extension portion (207, Fig 2). The insertion portion is dimensioned to be inserted into an aperture (601, Fig 6) of a dental implant surgical guide (602, Fig 6) and the shoulder is dimensioned to limit the extent of insertion of the sleeve into the aperture. Different sleeves can be used in different phases of drilling a socket for a dental implant, to systematically increase the diameter/depth of the socket. The collar may be attached to a standard drill to allow the said plurality of sleeves to be attached thereto.