It is generally agreed that the slow fluctuations in the envelope of speech in different spectral channels carry critical information for intelligibility. Previous studies in which amplitude modulation (AM) was selectively removed from the speech signal showed that modulation rates between 4 and 16 Hz are most important, and that rates falling outside this range contribute little or not at all to speech intelligibility. The present study investigated the role of very low (<4 Hz) AM rates in the ability to identify sentences in an interfering background talker. The mixture was processed through a noise vocoder. The depth of AM with rates below 4, 1.3, or 0.4 Hz was reduced using a multi-channel envelope compressor with a high compression ratio. Data obtained using nine normal-hearing listeners demonstrate that low-rate AM, in the range 0.4-4 Hz, contributes to the intelligibility of relatively long speech utterances, at least for adverse listening conditions in which background noise is present and listeners are forced to rely on envelope cues in a few spectral channels.