A square array of signal points forming a 22n-QAM signal constellation, where n=3, 4, is modified by relocating the inner most 22n/16 and outer 22n/16 constellation points to specific positions, resulting a modified-square constellation with a reduced peak to average power ratio (PAPR) at the modulator output relative to that of the square constellation while resulting in a receiver sensitivity that is degraded by less than the decrease in the modulator's PAPR and hence less than the possible improvement at the transmitter in average transmitted power.