The present invention provides a technique to reduce peak-to-average power ratio (PAR) of multi-carrier transmission systems. A non-empty subset of the subcarriers includes “PAR subcarriers.” The PAR subcarriers have constellations obtained by reducing a constellation that is higher than binary and invariant under multiplication by −1, so that an element is in the reduced constellation if and only if its negative is not. In this way, only one bit per PAR subcarrier is used for PAR reduction. The technique addressed in this invention multiplies a subset of the PAR subcarriers by −1 to reduce PAR at each multi-carrier symbol transmission. A method or apparatus is operated to select the subset of PAR subcarriers to be rotated. The receiver identifies the PAR subcarriers and estimates the subcarriers multiplied by −1 according to the reduced constellations and the received samples.