A driven appliance, such as a contra-angle handpiece for surgical instruments, in particular for dental surgery, includes a handle, a neck and a head for receiving an instrument. The handle and the neck of the contra-angle handpiece each receive a drive shaft, respectively, an input shaft and an output shaft, which are linked to each other by a gear train. The input shaft and the output shaft are slidingly mounted in their respective bodies, which forms a sheath for the two shafts. The shafts are maintained and supported on stops arranged on the corresponding sheathes through a single elastic element which is housed in the bend linking the handle to the neck.