The speech intelligibility index (SII) calculation is based on the assumption that the effective range of signal-to-noise ratio (SNR) regarding speech intelligibility is [− 15 dB; +15 dB]. In a specific frequency band, speech intelligibility would remain constant by varying the SNRs above + 15 dB or below − 15 dB. These assumptions were tested in four experiments measuring speech reception thresholds (SRTs) with a speech target and speech-spectrum noise, while attenuating target or noise above or below 1400 Hz, with different levels of attenuation in order to test different SNRs in the two bands. SRT varied linearly with attenuation at low-attenuation levels and an asymptote was reached for high-attenuation levels. However, this asymptote was reached (intelligibility was not influenced by further attenuation) for different attenuation levels across experiments. The − 15-dB SII limit was confirmed for highpass filtered targets, whereas for low-pass filtered targets, intelligibility was further impaired by decreasing the SNR below − 15 dB (until − 37 dB) in the high-frequency band. For high-pass and low-pass filtered noises, speech intelligibility kept improving when increasing the SNR in the rejected band beyond + 15 dB (up to 43 dB). Before reaching the asymptote, a 10-dB increase of SNR obtained by filtering the noise resulted in a larger decrease of SRT than a corresponding 10-dB decrease of SNR obtained by filtering the target (the slopes SRT/attenuation were different depending on which source was filtered). These results question the use of the SNR range and the importance function adopted by the SII when considering sharply filtered signals.