In a recently proposed communication system, there would be tandem connections of 16 kb/s delta modulators and 2.4 kb/s vocoders. Preliminary work has indicated that such tandem links would be of substantially lower quality than either the delta modulator link or the vocoder link alone. The present study, which includes an elaborate subjective speech quality experiment, confirms this preliminary conclusion. It also shows that two other differential waveform coders are no better than the proposed delta modulator in tandem links. On the other hand, a 5-band sub-band coder does offer substantially higher quality than the delta modulator. Still, its performance in tandem with the vocoder is poorer than that of the vocoder or the sub-band coder alone and is probably of only marginal value for practical communication. We have obtained several objective measures of speech quality which, for the most part, show relatively little correlation with subjective quality. The most successful objective predictor of subjective ratings is a linear combination of linear predictive coding distances.