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), spectral and energy efficient OFDM (SEE-OFDM), Hybrid-ACO-OFDM and Layered-ACO-OFDM. This paper presents simulations up to high-order constellation sizes to show that Layered-ACO-OFDM offers the highest receiver sensitivity for a given optical power at spectral efficiencies above 3 bit/s/Hz. For comparison purposes, white Gaussian noise is added at the receiver, component nonlinearities are not considered, and the fiber is considered to be linear and dispersion-less. The simulations show that LACO-OFDM has a 7-dB sensitivity advantage over DC-biased OFDM (DCO-OFDM) for 1024-QAM at 87.5% of DCO-OFDM's spectral efficiency, at the same bit rate and optical power. This is approximately equivalent to a 4.4-dB advantage at the same spectral efficiency of 87.7% if 896-QAM were to be used for DCO-OFDM.