The handover algorithms implemented in Network Simulator-3 (A3RSRP and A2A4RSRQ) for Long Term Evolution (LTE) so far, under certain scenarios, fail to prevent unnecessary handovers like ping-pong handovers which may lead to poor channel quality. To address this issue, we present A1A3RSRP (based on Reference Signal Received Power (RSRP)) and A1A2A4RSRPRSRQ (based on both RSRP and Reference Signal Received Quality (RSRQ)) handover algorithms. The primary objective of these algorithms is to reduce the number of unnecessary handovers such as ping-pong handovers which diminish the network performance. We compare and provide statistical analysis for these algorithms using various metrics and show that in a topology which induces ping-pongs, A1A3RSRP reduces the number of ping-pong handovers by an average of 33.33% as compared to A3RSRP and increases the average aggregate system throughput by an average of 3.43%. With the same topology, A1A2A4RSRPRSRQ reduces the number of ping-pong handovers by an average of 50% as compared to A2A4RSRQ and increases the average aggregate system throughput by an average of 3.38%. Also, on a realistic topology, A1A3RSRP reduces the number of ping-pong handovers by an average of 1.75% as compared to A3RSRP while maintaining the same average aggregate system throughput. In this topology, A1A2A4RSRPRSRQ reduces the number of ping-pong handovers by an average of 6.45% as compared to A2A4RSRQ without compromising the average aggregate system throughput. © 2017 IEEE.