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In this paper we present two results on reducing the peak power of orthogonal frequency division multiplexing (OFDM) symbols via constellation extension (CE). The first result is a derivation of the interior-point method (IPM) algorithm needed to find the optimal distortion set, where the distortion is constrained by convex functions. Next we optimize the parameters of a hybrid CE constraint set to minimize the BER. Numerical examples are provided to illustrate the findings.