Abstract: A traction-sheave elevator is provided without a counterweight. The elevator includes an elevator car that is guided in an elevator shaft. A rope is used to carry the car. The elevator further include at least two motor-driven traction-sheaves that are connected one behind the other relative to the rope. The rope wraps around each traction-sheave to define a relative angle of wrap greater than 180°. A tensioning device is connected downstream of the traction-sheaves for self-adjustably applying a requisite tension to the rope after the rope comes off the second traction-sheave. Additionally, a braking device is provided for at least one of the traction-sheaves.