Pulse-amplitude modulation (PAM) is extended to two and four dimensions by means of a nonlinear, memoryless mapping to obtain pulse-amplitude-and-phase modulation (PAPM). This modulation requires either the same bandwidth as double-sideband PAM or twice as much but yields a signal-to-noise ratio (SNR) improvement factor similar to that of FM with considerably less sacrifice of spectral occupancy. Several signal-space mappings are investigated for Gaussian data. Expressions for output SNR are derived in terms of a linear error above threshold and an anomalous threshold-producing error. PAPM is compared with various modulation techniques in terms of power and bandwidth requirements. The degradations in output SNR caused by carrier phase, carrier amplitude, and sample timing reference errors are evaluated so that requirements for demodulator design can be specified.