We present two multilevel constant-envelope continuous-phase modulation (CPM) schemes with four-dimensional (4-D) trellis coding. The receiver is composed of a simple quadrature demodulator, followed by a symbol-rate sampler and a Viterbi decoder matched to the code trellis. The first modulation is a quaternary CPM scheme whose phase transitions over a symbol interval are those of /spl pi//4-shift quaternary phase-shift keying (QPSK). The demodulator filter is optimized so as to minimize the combined effect of intersymbol interference (ISI) and noise at the decision instants. We use Wei's (1987) 16-state 4-D trellis code, and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation (QAM) signal sets. The resulting modulation outperforms minimum-shift keying (MSK) by as much as 3.5 dB, in addition to reducing the 30-dB signal bandwidth by 20%. Next, we introduce an octonary (8-level) CPM scheme whose phase transitions are those of /spl pi//8-shift 8PSK. The same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than MSK, while saving some 60% of the transmitted signal bandwidth.