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Orthogonal frequency division multiplexing (OFDM), has recently attracted considerable attention because of its features to combat delay spread or frequency selective fading of wireless or wireline channels. One of the major drawbacks of OFDM is the peak-to-average power ratio (PAPR) which leads to an inefficient use of high power amplifiers (HPA) in communications systems. The authors first briefly review the principle of geometric method (GM) that they previously proposed. This method has a couple of well identified drawbacks as the necessity of adding a radio frequency (RF) filter, the increasing of power amplifier band and the bit error rate degradation if PAPR is largely mitigated. Consequently we propose in this paper a new method to improve GM performance. This method mixes tone reservation (TR) technique and GM called `TR-GM` in order to efficiency reduce the high PAPR of OFDM signals. In addition, the proposed TR-GM technique is compared with TR based on second order cone programming (`TR-SOCP`) and TR based on the gradient-project (`TR-GP`) techniques in terms of PAPR reduction, average power variation and complexity. The comparative study has shown that, the proposed TR technique seems to be a good compromise between PAPR reduction, complexity, and average power variation.