Ueda and Nakajima [Trans. Tech. Comm. Psychol. Physiol. Acoust., 38, 771-776, (2008); 39, 211-216, (2009)] found a consistent clustering of frequency bands common to different languages through factor analyses applied to power fluctuations of critical-band filtered speech sounds. One of the factors exhibited a characteristic shape of two peaks, which implied a correlation between a pair of distant frequency bands. The present study examined how amplitude envelope independence across frequency bands affected perception of Japanese noise-vocoded speech. The results indicated that the 20- and 4-band-synthesis conditions exhibited nearly perfect performances without any systematic training or feedback, and that the conditions in which the lowest and the next lowest frequency band blended, keeping a long-term spectrum energy distribution (sharpness) constant, yielded low mora accuracy. Those results indicated that noise-vocoded speech synthesized with the 4 frequency bands contained enough information for speech perception.