An elevator system (20) includes a cab (22) supported for movement within a hoistway. A tension device (44) remains close to one end (26) of the hoistway. The tension device (44) maintains a desired tension on a load bearing member (30) that supports a weight of the cab (22) and moves to achieve a desired placement of the cab within the hoistway. The load bearing member (30) extends from the first end of the hoistway toward the cab, wraps at least partially around a first sheave (36) supported for movement with the cab, extends from the first sheave (36) toward the first end (24) of the hoistway, wraps at least partially around a second sheave (38) supported near the first end of the hoistway, extends from the second sheave toward a second end (26) of the hoistway, wraps at least partially about a third sheave (40) supported near the second end of the hoistway, extends toward the cab from the third sheave, wraps at least partially around a fourth sheave (42) supported for movement with the cab, and extends from the fourth sheave toward the second end of the hoistway where it is secured to the tension device (44).