A counterweightless elevator includes a hoistway, a car vertically movable in the hoistway, one or more suspension ropes, a rotatable drive member engaging said suspension rope(s), each of the suspension rope(s) having a first rope section on the first side of the drive member and a second rope section on the second side of the drive member, and each rope section being connected to the car, said first rope section suspending the car, and a tightening device arranged to tighten the second rope section. Each of said rope(s) is belt-like and includes a load bearing member or a plurality of load bearing members, which load bearing member(s) is/are made of composite material including reinforcing fibers embedded in a polymer matrix, which reinforcing fibers are carbon fibers.

A method of operating an elevator, the elevator having an elevator car, a motor, a controller and a counterweight (CW), the method including, for ascending of the elevator car when loaded with passengers, providing a car occupancy limiter (COL) and activating the COL by the controller for ensuring that the loaded car weighs less than the CW and controlling by the controller of the motor to not use motor rotational power; and for descending of the elevator car when loaded with passengers, where the loaded car weighs more than the CW, controlling by the controller of the motor to not use motor rotational power.