An elevator system (20) includes a tie-down compensation arrangement (40). A tension member (42) extends between a cab (22) and counterweight (26) to provide a desired amount of tension on a load bearing rope or belt (30) that supports the cab and the counterweight. The tension member (42) in one example comprises a coated steel belt. At least one sheave (46) is supported on a base module (48) and remains stationary relative to a floor of a pit (52). A damper (50) is supported for movement with the counterweight (26) or the cab (22) to absorb energy that would otherwise tend to cause counterweight jump following a rapid descent and stop of the cab (22).