A method for reducing peak-to-average power ratio in an OFDM signal, the method comprising: a) quadrature amplitude modulating, QAM, a signal including a set of subcarriers with a set of data to produce an orthogonal frequency division multiplexed, OFDM, modulated symbol vector; b) limiting the magnitude of the modulated symbol vector to produce a first limited OFDM modulated symbol vector; c) demodulating the first limited OFDM modulated symbol vector to recover distorted QAM constellations; d) constraining points in the distorted QAM constellations recovered from the first limited OFDM modulated symbol vector to produce constrained QAM constellations wherein: points at corners of the distorted QAM constellations are constrained both in-phase and in-quadrature to values greater than or equal to a first minimum threshold; points along edges, but not corners , of the distorted QAM constellations are constrained to either in-phase values greater than or equal to a second minimum threshold value and in quadrature to a first predetermine range of values on either side of the undistorted constellation point, or in-quadrature to values greater than or equal to a third minimum threshold value and in phase to a second predetermine range of values on either side of the undistorted constellation point; and internal points of the distorted QAM constellations are constrained to both in-phase and in-quadrature values less than or equal to a third predetermined range of values on either side of the undistorted constellation point; e) modulating the OFDM symbol vector with the constrained QAM constellations to produce a modified modulated OFDM symbol; and f) output the modified modulated OFDM symbol. a) quadrature amplitude modulating, QAM, a signal including a set of subcarriers with a set of data to produce an orthogonal frequency division multiplexed, OFDM, modulated symbol vector; b) limiting the magnitude of the modulated symbol vector to produce a first limited OFDM modulated symbol vector; c) demodulating the first limited OFDM modulated symbol vector to recover distorted QAM constellations; d) constraining points in the distorted QAM constellations recovered from the first limited OFDM modulated symbol vector to produce constrained QAM constellations wherein: points at corners of the distorted QAM constellations are constrained both in-phase and in-quadrature to values greater than or equal to a first minimum threshold; points along edges, but not corners , of the distorted QAM constellations are constrained to either in-phase values greater than or equal to a second minimum threshold value and in quadrature to a first predetermine range of values on either side of the undistorted constellation point, or in-quadrature to values greater than or equal to a third minimum threshold value and in phase to a second predetermine range of values on either side of the undistorted constellation point; and internal points of the distorted QAM constellations are constrained to both in-phase and in-quadrature values less than or equal to a third predetermined range of values on either side of the undistorted constellation point; e) modulating the OFDM symbol vector with the constrained QAM constellations to produce a modified modulated OFDM symbol; and f) output the modified modulated OFDM symbol. <EOS>