In the context of cognitive radio, this paper proposes a simple spectral precoding for orthogonal frequency-division multiplexing (OFDM) to suppress its out-of-band radiation for a better adjacent-channel coexistence. Additionally, the proposed scheme is also aimed to improve the in-band subcarrier notching to efficiently utilize the fragmented spectrum. Through the proper system modeling and optimal selection for the precoder's weights, it is demonstrated to achieve a much better spectral compactness than the conventional OFDM, meanwhile possess only a trivial cost for computational complexity. Compared with other OFDM variant schemes, it is thereby concluded that the proposed scheme can be one of the promising candidates for the physical layer of future's cognitive radio devices.