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The high peak-to-average power ratio (PAR) in orthogonal frequency division multiplexing (OFDM) modulation systems can significantly reduce power efficiency and performance. Methods exist which alter or introduce new signal constellations to combat large signal peaks. We present a new PAR-reduction method that dynamically extends outer constellation points in active (data-carrying) channels, within margin-preserving constraints, in order to minimize the peak magnitude. This scheme simultaneously decreases the bit error rate slightly while substantially reducing the peak magnitude of an OFDM transmit block. Furthermore, there is no loss in data rate and, unlike other methods, no side information is required. PAR reduction for an approximated analog signal is considered, and about a 4.6 dB reduction at a 10-5 symbol-clip probability is obtained for 256-channel QPSK OFDM. The results show great promise for use in commercial systems.