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Intelligibility is an important concern of speech transmission channels. The paper addresses speech intelligibility issues in the VoIP to PSTN interworking context, discusses the complexity of quantifying speech intelligibility, and advocates speech based objective assessments. The limitations of mean opinion score (MOS) centred quality indices are discussed. A dedicated intelligibility index seems to be more useful in some cases than a general opinion index. Although objective intelligibility assessment methods, such as speech transmission index (STI) and speech intelligibility index (SII), for rooms, public address systems, and other continuous channels are inadequate for channels involving packetised networks and non-linear codecs, they are closely related to the physical characteristics of transmission channels and intelligibility. A framework derived from the STI method is rationalised and might be used to achieve objective, speech-based, and non-intrusive assessment of speech intelligibility of telephony channels involving packetised networks.