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This paper deals with the optimization of coherent generalized tamed frequency modulation (GTFM). The optimization is carried out over certain parameters of the modulation scheme to give the best BER (bit error rate) performance, subject to a bandwidth constraint. The optimization is done by an algorithm which uses the upper bound on the squared Euclidean distance as a metric of the BER performance and the power spectra at a certain frequency as a metric of the bandwidth. It is concluded that when the modulation index is not restricted to 0.5, a theoretic improvement of 1.9 dB over the BER performance of GTFM is achievable, with equal bandwidths as a basis of comparison.