A dedicated endodontic handpiece (20) includes a hollow body portion (21) accommodating a low-speed motor, and a first mechanical transmission element (22) coupled to the motor shaft. A disposable head portion (25) is adapted for removably coupling to the end (23) of the body portion and accommodates at a first end a second mechanical transmission element (26) for engaging the first mechanical transmission element (22) when the head portion is coupled to the body portion. A connector (30) at a second end of the head portion frictionally grips an endodontic tool (31) without any other locking means; and an electronic control circuit within the body portion controls the motor speed as a function of load and resistance applied by the root canal through the endodontic tool to the motor.