The distribution of the peak-to-average power (PAP) ratio of an OFDM signal is derived, showing that large PAP ratios only occur very infrequently. Because of this, PAP reducing techniques which distort the signal can be quite effective, since only a small fraction of the OFDM signal has to be distorted. One example of such a technique is peak windowing. It is shown that peak windowing can achieve PAP ratios around 4 dB for an arbitrary number of subcarriers, at the cost of a slight increase in the BER and out-of-band radiation. Simulations with realistic power amplifier models show that a backoff of about 5 dB is required to get an out-of-band radiation level of 30 dB below the in-band spectral density.