DSI (digital speech interpolation) is a technique for increasing the utilization of telephone transmission facilities by allocating transmission channels during intervals of active speech (talkspurts) only. The use of DSI for tandem connections, where DSI links are connected in cascade via circuit switching, poses a problem, however, since the voice-quality degradation that is inevitable in each DSI link can be accumulated to an unacceptable level as the number of DSI links in an end-to-end call connection increases. To cope with this problem, we propose the use of a priority channel assignment technique. An example of such a technique is one that provides preference in channel assignment at each DSI process in a network to calls that have passed through at least one prior DSI link. We evaluate the performance of priority assignment schemes for TASI-type DSI analytically and show that the overall voice-quality degradation of a multi-DSI link call can be improved significantly through the use of priority assignment.