Time-reversed orthogonal frequency division multiplexing (TR-OFDM) has recently received attention as a promising scheme for supporting single-input multiple-output (SIMO) communications over time-dispersive fading channels. In TR-OFDM, the time reversal processing cleverly converts multiple time-dispersive fading channels associated with SIMO-OFDM into a single channel with generally smaller time dispersion and less fading. As a result, a moderate cyclic-prefix (CP) length can be used without inducing much inter-block interference (IBI) even when the original channels are long. This paper tackles a technical challenge critical to the success of TR-OFDM, that is, how to minimize the CP length while satisfying certain performance requirements. Based on a data model derived for TR-OFDM, a quantitative relationship between the CP length and error performance is first established and a design procedure is then proposed. Our design reveals that the optimal CP length depends on the power delay profiles of underlying channels. Both theoretical analysis and numerical simulations confirm the merits of our design.