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This paper proposes an optimized delay diversity (ODD) scheme for frequency-selective fading channels. The novel scheme requires knowledge of the channel impulse response (CIR) autocorrelation matrix at the transmitter, but the CIRs themselves have to be available only at the receiver side. A cost function for optimization of the ODD transmit filters is derived and a steepest descent algorithm for iterative calculation of the filter coefficients is provided. In addition, an upper bound on the cost function is derived and employed to prove the asymptotic optimality of the generalized DD (GDD) scheme in [Proc. IEEE Int. Conf. Communications (ICC), (2002) p. 1949] for very high signal-to-noise ratios (SNRs) and transmit filters of maximum length. However, for SNRs of practical interest and reasonable filter lengths, the novel ODD scheme significantly outperforms GDD for both optimum and suboptimum equalizations. It is also shown that, in contrast to the frequency-nonselective case, for frequency-selective channels, transmit diversity schemes designed under the high SNR assumption may perform poorly for practically relevant SNRs.