Peak-to-average power-ratio (PAPR) reduction for OFDM systems is investigated in a probabilistic framework. A new constellation extension technique is developed whereby the data for each subcarrier are represented either by points in the original constellation or by extended points. An optimal representation of the OFDM signal is achieved by using a de-randomization algorithm where the conditional probability involved is handled by using the Chernoff bound and the evaluation of the many hyperbolic cosine functions involved is replaced by a tight upper bound for these functions. The proposed algorithm can be used by itself or be combined with a selective rotation technique described in the paper and with other known algorithms such as the coordinate descent optimization and selective mapping algorithms to achieve further performance enhancements at the cost of a slight increase in the computational complexity. When compared with other existing PAPR-reduction algorithms, the enhanced algorithm offers improved PAPRreduction performance and improved computational complexity although the transmit power is increased somewhat.