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It has recently been shown that by altering the sign of each subcarrier in a multicarrier system significant reduction in the peak to mean envelope power (PMEPR) can be obtained. In fact, the PMEPR can even be made a constant independent of the number of subcarriers n. However, finding the best sign requires a search over 2n possible signs which is computationally prohibitive. In this paper, we first propose a greedy algorithm to choose the signs based on p-norm minimization and we prove that it can achieve a PMEPR of order log n. We further decrease the PMEPR by enlarging the search space considered by the greedy algorithm. By ignoring peaks with probability less than 10-3, simulation results show that the PMEPR of a multicarrier system with 128 subcarriers each one modulated by 64QAM constellations is reduced to 3.4. This implies that at the cost of one bit of information per subcarrier (i.e., not sending information over the sign of each subcarrier) and modest computational complexity in the transmitter, the PMEPR can be reduced from 12.5 to 3.4 which is within 1.6 dB of the PMEPR of a single carrier system with 64QAM modulation.