Band-importance functions were created using the "compound" technique [Apoux and Healy, J. Acoust. Soc. Am. 132, 1078-1087 (2012)] that accounts for the multitude of synergistic and redundant interactions that take place among speech bands. Functions were created for standard recordings of the speech perception in noise (SPIN) sentences and the Central Institute for the Deaf (CID) W-22 words using 21 critical-band divisions and steep filtering to eliminate the influence of filter slopes. On a given trial, a band of interest was presented along with four other bands having spectral locations determined randomly on each trial. In corresponding trials, the band of interest was absent and only the four other bands were present. The importance of the band of interest was determined by the difference between paired band-present and band-absent trials. Because the locations of the other bands changed randomly from trial to trial, various interactions occurred between the band of interest and other speech bands which provided a general estimate of band importance. Obtained band-importance functions differed substantially from those currently available for identical speech recordings. In addition to differences in the overall shape of the functions, especially for the W-22 words, a complex microstructure was observed in which the importance of adjacent frequency bands often varied considerably. This microstructure may result in better predictive power of the current functions.