We study the properties of optical single-sideband (SSB) modulation with respect to signal-to-noise ratio and limits to spectral efficiency. We show that SSB signals undergo truly noiseless amplification, which can be understood in view of Heisenberg's uncertainty principle. Yet, contrary to previously published results, this phenomenon offers no advantages in terms of the signal-to-noise ratio of the amplified signal. We show that, when an intensity receiver is used, single-sideband modulation can improve spectral efficiency in the limit of a high optical signal-to-noise ratio and in the presence of a strong carrier signal.