An elevator comprising a hoistway; an elevator car vertically movable in the hoistway; a counterweight vertically movable in the hoistway; at least one rope wheel located in or at least in proximity of the upper end of the hoistway; a first roping interconnecting the car and counterweight and passing around the at least one rope wheel located in or at least in proximity of the upper end of the hoistway; at least one tightening wheel located in the lower end of the hoistway; a second roping interconnecting the car and counterweight and passing around the at least one tightening wheel, the tightening wheel being mounted movably back and forth in a first direction towards the second roping, and in a second direction away from the second roping; and means (5,5') for exerting force (F 5,F 5') on the tightening wheel to move it in the first direction so as to tighten the second roping; and means (F,6,7,10,12;F,6',7,10',12';F,6a,6b,7,10',12a,12b;F,6a',6b', 7,12a',12b') for limiting the movement speed of the tightening wheel towards the first direction and the second direction. wherein said means (F,6,7,10,12;F,6',7,10',12'; F,6a,6b,7,10',12a,12b;F,6a',6b',7,12a',12b') for limiting the movement speed of the tightening wheel towards the first direction and the second direction comprise a frame mounted in the hoistway and a hydraulic cylinder containing hydraulic fluid and being mounted between the frame and the tightening wheel, one of its piston part and cylinder part being attached to the frame, and the other of its piston part and cylinder part being attached to the tightening wheel, movement of the tightening wheel in said first direction being configured to cause a stroke of the hydraulic cylinder wherein the piston moves in the cylinder part in a first stroke direction, and movement of the tightening wheel in said second direction being configured to cause a stroke of the hydraulic cylinder wherein the piston moves in the cylinder part in a second stroke direction, and in that said means for limiting the movement speed comprise means (6,10,12; 6',10',12';6a,6b,10',12a,12b; 6a',6b',12a',12b') for limiting stroke speed of the cylinder in the first and second stroke direction, and in that said means (6,10,12;6',10',12';6a,6b,10',12a,12b;6a',6b',12a',12b') for limiting stroke speed of the cylinder comprises a conduit system (12;12';12a,12b;12a',12b') connected with an opening (10;10') in the hydraulic chamber (11;11') delimited by the piston part and the cylinder part, characterised in that said means (6,10,12; 6',10',12'; 6a,6b,10',12a,12b; 6a',6b',12a',12b') for limiting stroke speed of the cylinder further comprises one or more adjustable flow control valves (6;6';6a,6b;6a',6b') in the conduit system (12;12';12'12a,12b;12a',12b'), and in that each of the stroke in said first direction and the stroke in the second stroke direction is arranged to change the volume of the hydraulic chamber (11;11'), and to displace an amount of hydraulic fluid through said opening (10;10') and through at least one of said adjustable flow control valves (6;6';6a,6b;6a',6b'), which amount is equal to the amount of change of the volume of the hydraulic chamber (11;11'). a hoistway; an elevator car vertically movable in the hoistway; a counterweight vertically movable in the hoistway; at least one rope wheel located in or at least in proximity of the upper end of the hoistway; a first roping interconnecting the car and counterweight and passing around the at least one rope wheel located in or at least in proximity of the upper end of the hoistway; at least one tightening wheel located in the lower end of the hoistway; a second roping interconnecting the car and counterweight and passing around the at least one tightening wheel, the tightening wheel being mounted movably back and forth in a first direction towards the second roping, and in a second direction away from the second roping; and means (5,5') for exerting force (F 5,F 5') on the tightening wheel to move it in the first direction so as to tighten the second roping; and means (F,6,7,10,12;F,6',7,10',12';F,6a,6b,7,10',12a,12b;F,6a',6b', 7,12a',12b') for limiting the movement speed of the tightening wheel towards the first direction and the second direction.