The Speech Intelligibility Index (SII) assumes additivity of the importance of acoustically independent bands of speech. To further evaluate this assumption, open-set speech recognition was measured for words and sentences, in quiet and in noise, when the speech stimuli were presented to the listener in selected frequency bands. The filter passbands were constructed from various combinations of 20 bands having equivalent (0.05) importance in the SII framework. This permitted the construction of a variety of equal-SII band patterns that were then evaluated by nine different groups of young adults with normal hearing. For monosyllabic words, a similar dependence on band pattern was observed for SII values of 0.4, 0.5, and 0.6 in both quiet and noise conditions. Specifically, band patterns concentrated toward the lower and upper frequency range tended to yield significantly lower scores than those more evenly sampling a broader frequency range. For all stimuli and test conditions, equal SII values did not yield equal performance. Because the spectral distortions of speech evaluated here may not commonly occur in everyday listening conditions, this finding does not necessarily represent a serious deficit for the application of the SII. These findings, however, challenge the band-independence assumption of the theory underlying the SII.