The short-time Fourier transform (STFT) of a speech signal has two components: the magnitude spectrum and the phase spectrum. In this paper, the relative importance of short-time magnitude and phase spectra for speech perception is investigated. Human perception experiments are conducted to measure intelligibility of speech stimuli synthesized either from magnitude spectra or phase spectra. It is traditionally believed that the magnitude spectrum plays a dominant role for small window durations (20-40~ms); while the phase spectrum is more important for large window durations (> 1 s). It is shown in this paper that even for small window durations, the phase spectrum can contribute to speech intelligibility as much as the magnitude spectrum if the analysis-modification-synthesis parameters are properly selected.