In a method and an elevator of the invention, the elevator is preferably an elevator without machine room, in the elevator an elevator car is at least partially supported by a set of hoisting ropes. The hoisting ropes comprise one rope or a number of parallel ropes. The elevator has a traction sheave which moves the elevator car by means of the hoisting ropes. The elevator comprises rope portions of hoisting ropes going upwards and downwards from the elevator car, and the rope portions going upwards from the elevator car are under a first rope tension (T1) and the rope portions going downwards from the elevator car are under a second rope tension (T2). The elevator has a compensating device acting on the hoisting ropes to equalize and/or compensate rope tension and/or rope elongation and/or to render the ratio (T1/T2) of the first and the second rope tensions substantially constant. The compensating device comprises an arrangement producing an auxiliary force acting substantially in the same direction with the first rope tension (T1).