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Digital satellite communication has been restricted to date to digital modulations having an efficiency of 2 bps/Hz; that is, filtered-QPSK with a close to constant envelope. The main limitation to higher-order digital modulations is the need for linearity of a high power amplifier in both the satellite and the terminal. Many years ago, C.M. Thomas et al. (see IEEE Trans. Commun., vol.COM-22, p.168-80, 1974) conducted a complete study of the use of higher-order linear modulations on nonlinear satellite channels. However, pulse-shaping and predistortion were not treated. We consider these items for amplitude-phase-shift-keying (APK) modulation, that is, signal points assigned on concentric circles. We consider both single- and double-link channels. Our best result is for a single-link channel and (5,11)-APK (5 points on an inner circle and 11 on the other), which, for predistortion on the nonlinear channel, loses only about 1 dB to 16-QAM transmission on the linear channel. Our results for single-link, narrow band channels are felt to be generally applicable to narrowband wireless communication channels.