Miniaturized NMR is of growing importance in bio-, chemical, and -material sciences. Other than the magnet, bulky components are the radio-frequency power amplifier and the power supply or battery pack. We show that constant flip-angle excitation with phase modulation following a particular type of polyphase perfect sequences results in low peak excitation power at high response peak power. It has ideal power distribution in both the time domain and the frequency domain. A savings in peak excitation power of six orders of magnitude has been realized compared to conventionally pulsed excitation. Among others, the excitation promises to be of use for button-cell operated miniature NMR devices as well as for complying with specific-absorption-rate regulations in high-field medical imaging.