Recently, a very effective peak-to-average power ratio (PAR) reduction scheme based on the distribution transform (DT) for OFDM signals is proposed. Key idea of DT is to transform the distribution of the OFDM signal amplitudes into a target distribution, which has limited dynamic range and very low PAR. But, the PAR-reduction performance and the BER performance of DT are conflicting with each other similar to other signal-distortion-type PAR-reduction schemes. In this paper, the trade-off between the PAR and BER performances of DT is addressed. An analysis framework is proposed to select the optimum transform function for DT with minimum consumed energy-to-noise ratio (SNRC). Simulation shows DT with the optimum transform function can obtain about 2dB SNRC gain compared to the original OFDM signal.