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The design of a routing protocol for Unmanned Aeronautical Ad-hoc Networks (UAANETs) is a great challenge, especially due to the high mobility of Unmanned Aerial Vehicles (UAVs). Among all routing protocols that have been designed for UAANETs, the Reactive-Greedy-Reactive (RGR)  protocol has been proposed as a promising routing protocol in high mobility and density-variable scenarios. However, the main drawback of the RGR protocol is its high overhead due to the exchange of control messages associated with multiple route requests. In this paper, two enhancement strategies, namely scoped flooding and delayed route request, are proposed to reduce overhead. Simulation results show that both modifications can enhance the RGR protocol in terms of overhead, packet delivery ratio and delay respectively.