A constrained-envelope digital-communications transmitter circuit (22) in which a binary data source (32) provides an input signal stream (34), a phase mapper (44) maps the input signal stream (34) into a quadrature phase-point signal stream (50) having a predetermined number of symbols per unit baud interval (64) and defining a phase point (54) in a phase-point constellation (46), a pulse-spreading filter (76) filters the phase-point signal stream (50) into a filtered signal stream (74), a constrained-envelope generator (106) generates a constrained-bandwidth error signal stream (108) from the filtered signal stream (74), a delay element (138) delays the filtered signal stream (74) into a delayed signal stream (140) synchronized with the constrained-bandwidth error signal stream (108), a complex summing circuit (110) sums the delayed signal stream (140) and the constrained-bandwidth error signal stream (108) into a constrained-envelope signal stream (112), and a substantially linear amplifier (146) amplifies the constrained-envelope signal stream (112) and transmits it as a radio-frequency broadcast signal (26).