Asymmetrically clipped optical orthogonal frequency-division multiplexing (ACO-OFDM) is a technique that sacrifices spectral efficiency in order to transmit an orthogonally frequency-division multiplexed signal over a unipolar channel, such as a directly modulated direct-detection fiber or free-space channel. Several methods have been proposed to regain this spectral efficiency, including: asymmetrically clipped DC-biased optical OFDM (ADO-OFDM), enhanced U-OFDM (EU-OFDM), and spectral and energy efficient OFDM (SEE-OFDM). This paper presents a new method that offers the highest receiver sensitivity for a given optical power at spectral efficiencies above 3 bit/s/Hz, having a 7-dB sensitivity advantage over DC-biased OFDM for 1024-QAM at 87.5% of its spectral efficiency, at the same bit rate and optical power.