Adaptive spectrally precoded orthogonal frequency-division multiplexing (ASP-OFDM) is a recently proposed adaptive modulation scheme to significantly improve the system throughput in adaptive OFDM applications. In this paper, new spectral precoder is proposed for ASP-OFDM with cyclic prefix (ASP-CP-OFDM) on the flat fading channel. By jointly adapting the precoding order for spectral precoder and the component modulation, the proposed ASP-CP-OFDM is shown to outperform adaptive nonprecoded OFDM and previously designed ASPCP-OFDM significantly in average spectral efficiency.