An elevator system (20) includes an elongated member (30, 32, 34) that may sway under certain conditions. An exemplary method of controlling the elevator system (20) includes selectively controlling an elevator car dispatching schedule when a condition exists that is conducive to sway of one of the elongated members (30, 32, 34). The control over the elevator car dispatching schedule controls the time that the elevator car is in a predetermined critical zone while the condition exists such that the time does not exceed a selected amount.