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In this paper, the specific-band power minimization precoding technique is incorporated with spectrally precoded OFDM to suppress near spectral sidelobes more efficiently and thus improve the spectral compactness. When the total number of redundant symbols introduced by both spectral precoder and specific-band power minimization precoder is fixed, the proposed OFDM system can find a balance between near sidelobe power suppression capability and sidelobe decaying capability to meet the desired spectral performance by properly allocating redundancy to the two precoders.