In one embodiment, the present invention is a method for reducing the peak-to-average power ratio (PAPR) of a multi-carrier modulated symbol, such as an orthogonal frequency division multiplexed (OFDM) symbol. The method first transforms a set of data symbols into a multi-carrier modulated symbol. The method then uses the multi-carrier modulated symbol and a gradient-descent algorithm to generate a set of symbols for PAPR-reduction tones. The data symbols and the PAPR-reduction symbols are then transformed to generate an updated multi-carrier modulated symbol. The PAPR-reduction symbols are iteratively updated until a terminating condition occurs (e.g., an acceptable PAPR is achieved for the multi-carrier modulated symbol). In another embodiment, the method uses the multi-carrier modulated symbol generated in the first step and a gradient-descent algorithm to generate an updated multi-carrier modulated symbol directly, where the need for transforming the data symbols and the PAPR-reduction symbols is eliminated for subsequent iterations.