An arrangement for driving a rotary dental or medical tool attached to a handpiece includes a vane motor that is compact enough to be mounted within the head of the handpiece. The vane motor includes a rotor, which is mounted within an eccentric bore of a cylinder, which forms a stator. Inlet ports into the vane motor preferably open perpendicular to the rotor's axis of rotation so that intake air is directed substantially directly at the vanes. An arrangement of the inlet and of outlet ports allows a duty stroke for each vane up to 240 degrees. Inlet and exhaust air preferably enters and exits the vane motor via annular channels surrounding either end of the cylinder. There is then no need to align the motor angularly when it is installed in the head. A radial gap is preferably provided between the rotor and the shaft it is mounted on. Channels connecting the bottom of each vane slot with this gap reduce the vacuum effect acting on the vanes as they extend. The rotor can preferably also move a small longitudinal distance of the shaft so that it can find its own balance position. The speed of the vane motor can be varied using a user-controller pressure controller.