This letter presents a simple and effective peak reduction method to achieve a desired peak-to-average power ratio (PAPR). The method is called phase on demand in which a fixed phase vector is added to input vectors only if it helps reduce the peak of the orthogonal frequency-division multiplexing (OFDM) signal otherwise no phase is added. Repeated clipping and filtering is applied whenever the PAPR exceeds a desired value. To avoid sending side information about the phase, a maximum-likelihood phase detector is derived. Simulation results show that the new method is an efficient peak reduction technique for coded OFDM (COFDM).