The invention concerns a handpiece for a surgical or dental tool (3), which can be inserted in the head of the handpiece (1) through an insertion hole (14) into a tool holder (2) and is rotationally supported by means of two axially separated bearings (12, 13), with positive torque transmission (8) to the tool (3) by the drive (9) installed in the handpiece, such that the tool possibly has a longitudinal bore (6) for supplying cooling liquid to the work site, and the handpiece (1) possibly has a short, fixed feed tube (7), which extends into the longitudinal bore and is sealed from the tool (3).To increase the torque that can be transmitted, the invention is characterized by the fact that the torque transmission (8) occurs in the region of the bearing (13) that is adjacent to the insertion hole (14).The invention also concerns the development of suitable tools.