The tensioning system for the traction belt of an elevator is installed or can be installed in connection with the car and/or the counterweight of the elevator for pretensioning at least one traction belt running between these and comprises means for storing energy. In addition to this, the tensioning system is configured to use the energy stored in the means intended for storing energy for pulling in the traction belt in question for returning tension when the tension of the traction belt falls.The patent application also contains an independent claim for an elevator.