The peak power problem in multicarrier waveforms is well-known and imposes substantial limitations on wireless communications. As the quest for investigation of enabling technologies for the next generation of wireless communication systems 5G is at its peak, the problem is re-emerging in a much broader range of technologies. However, despite numerous publications on the topic, there is no well-established structure available for the problem, which motivates a boost in research. In this paper, a novel peak power reduction algorithm is proposed which offers a substantial Peak-to-Average Power Ratio (PAPR) reduction and exhibits high potential for further refinements. Mathematical tractability of the algorithm is expected to be of particular importance to this end. A remarkable early observation is a PAPR reduction of about 4.5 dB for 64 subcarriers with a rate loss of 0.5 bits per complex data symbol in an OFDM scheme, which is half the rate loss that other methods require in this class of algorithms.