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Communication systems using multicarrier modulation suffer from a high peak-to-peak ratio, PAR. In this work we use the tone reservation approach to PAR reduction, where a subset of the tones are used for PAR reduction. We derive a bound on the achievable performance under a PSD constraint on the transmit signal. Using this bound, we show that as long as a moderate reduction performance is needed, this could be achieved with an almost arbitrary selection of the PAR reduction tones. This bounding technique also demonstrates that, applied to an ADSL-like system, the tone reservation approach could be used for PAR reduction down to about 12 dB, considering critically sampled signals.