In this paper, we study the effect of using or disengaging the RTS/CTS dialogue in IEEE 802.11 DCF MAC protocol incorporating the realistic condition under which carrier sensing, transmission and interference ranges are distinctively different. We present an algorithm that is employed independently by each network node, under which each node adaptively engages or disengages the RTS/CTS dialogue, depending upon the comparison of a Waiting-for-CTS-timeout count with a threshold level. We demonstrate that the new control mechanism used here to adaptively select the use of the RTS/CTS dialogue can improve throughput performance and fairness for both UDP and TCP traffic flows.