The generation of single-sideband angle-modulated (SSB-phiM) waves compatible with conventional detection methods requires involved processing. The result of these operations yields a signal whose spectral properties are more complicated than simply being one-sided versions of the analogous double-sideband spectrum, and hence it is not obvious whether or not a saving in bandwidth results. Here the spectral properties of SSB-phiMwaves are investigated in detail when the modulating signal is a sample function of a stationary Gaussian process. It is shown that the power spectrum of SSB-phiMis related to the modulating baseband spectrum through an integral equation. This equation is solved explicitly for small and large modulating indices, and it is shown how simple numerical techniques provide solutions for arbitrary index. It is concluded that SSB-phiMexhibits properties very similar to SSB-AM with a strong carrier component When the modulation index is much less than unity. Therefore, if minimum bandwidth plus the attributes of incoherent demodulation are desired, and a Strong carrier can be tolerated, SSB-phiMcould find an application. On the other hand, for modulation indices larger than about 3, no advantage is gained since the SSB spectrum has a bandwidth equal to or larger than the bandwidth of conventional angle-modulated waves.