Orthogonal frequency division multiplexing (OFDM) and discrete multitone (DMT) modulation offer many advantages for digital data transmission and have been adopted for several important standards. Their primary drawback is a high peak-To-Average power ratio (PAR). Methods which introduce compensation signals in unused channels, first developed by Gatherer and Polley (see Proceedings of the 31st Asilomar Conference on Signals, Systems, and Computers, p.578-84, 1997), are among the more promising methods for reducing the PAR. However these methods apply only to systems with unused channels or require the sacrifice of data rate for PAR reduction. We present a new method for PAR reduction using active (data-carrying) channels which dynamically moves outer constellation points, within margin-preserving constraints, to minimize the peak magnitude. This scheme simultaneously decreases the bit error rate slightly while substantially reducing the peak magnitude; simulations show peak reductions of slightly more than 6 dB.