Optimal relay settings are determined where coordination constraints are modelled considering only either one fault location (near end or midpoint) or two fault locations (near and far end) on a feeder. This study, first, investigates whether considering one or two fault locations is sufficient to guarantee proper coordination for faults at all other locations on a feeder. The results show that violations, in the coordination constraints, can occur at various points along the feeder if the relays are coordinated considering one or two fault locations. In addition, considering multiple fault locations while determining the optimal relay setting can avoid such problem but on the expense of the overall relay tripping time. Thus, a dual-setting characteristic for directional overcurrent relays (DOCRs) is proposed instead of the conventional inverse time-current characteristic. The study is conducted on the power transmission system of IEEE 24-bus and the power distribution system of IEEE 14-bus. The proposed characteristic achieves notable reduction in total DOCRs operating time over the conventional characteristic for both test systems while achieving proper coordination across a broader range of possible fault locations.