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A major drawback of orthogonal frequency division multiplexing (OFDM) is the high peak-to-average power ratio (PAPR) of the transmit signal which can significantly impact power efficiency and performance. In this paper we present a PAPR reduction technique which exploits the phase of the signal in the frequency domain. When used to extend a previous PAPR reduction technique developed by the authors, a PAPR reduction of up to 5 dB can be obtained with this technique giving extremely low out-of-band distortion as well as lower in-band distortion than windowing and clipping methods. There is also no need for side information to be transmitted to the receiver.