The problem of obtaining a one-sided spectrum by means of a combination of amplitude and phase modulation of a carrier is examined with particular reference to the question of compatibility with the a.m. method of transmission and reception.The spectrum of composite modulation, when the phase modulation is introduced either directly or indirectly, has been analysed for both single-tone and two-tone signals. The analysis indicates that, while it is possible to eliminate one of the two sideband components of a composite modulated wave, new components on the desired side of the carrier appear which have the character of the spectrum caused by single-sideband modulation of a carrier by the squared signal and the squared envelope.Some practical arrangements which enable maintenance of the required relationship between the amplitude- and phase-modulating signals for compatible-single-sideband operation have been described. The experimental results obtained for the different systems indicate that, for modulation by speech-like signals, the undesired radiation under normal conditions of modulation can be kept below 1% of the carrier, and the spectrum of the output is confined, as in single sideband, to the band of modulating frequencies.