Current objective measures for predicting the intelligibility of speech by an index assume that this can be obtained by simple addition of the contributions of individual frequency bands. The Articulation Index (AI, and the related Speech Intelligibility Index), and the Speech Transmission Index (STI) are based on this assumption. There is evidence that the underlying assumption of additive (mutually independent) contributions from a number of frequency bands is not optimal and may lead to erroneous prediction of the intelligibility for conditions with a limited or with a discontinuous frequency transfer. Depending on the frequency band considered, errors between 0.1 and 0.25 STI may occur. An experiment was designed to estimate the contribution of individual frequency bands, and their mutual dependence. For this purpose the speech spectrum was subdivided into seven octave bands with center frequencies ranging from 125 Hz to 8 kHz. For 26 different combinations of three or more octave bands the CVC-word score (Consonant-Vowel-Consonant, nonsense words) was determined at three signal-to-noise ratios. It was found that successful prediction of the scores required a revised model which accounts for mutual dependency between adjacent octave bands. In this model a so-called redundancy correction is introduced. Consequences for the existing objective measures are discussed. The presented results are included in the revised IEC standard (IEC 60268-part 16, 1998).