Visible light communications (VLCs) have received extensive attention in the research community thanks to their advantages of high bandwidth, low cost, robustness to electromagnetic interference, operation in an unregulated spectrum, and high degree of spatial confinement in indoor scenarios. One of the main limitations for high data-rate transmission in VLC systems is the limited modulation bandwidth of commercial light emitting diodes. To circumvent this limitation, spectrally efficient modulation schemes should be used. Optical orthogonal frequency-division multiplexing (O-OFDM)-based schemes have become very popular and several proofs of concept have shown their ability to attain over gigabits per second transmission rates. We consider here the use of pulse amplitude modulation and carrier-less amplitude and phase modulation schemes together with frequency-domain equalization (FDE) at the receiver as interesting alternatives to O-OFDM. We show the advantages of the former schemes in terms of the peak-to-average-power ratio, and demonstrate through numerical results the merits of FDE-based signaling in attaining high data rates.