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A critical component of computer communications networks is local distribution, i.e., techniques for connecting geographically dispersed users to a central facility. A drawback to conventional polling techniques for local distribution is excessive overhead. Thus, in systems with many lightly loaded terminals, message delay is more a function of the time required to poll all terminals than of traffic from competing sources. A technique for reducing overhead is presented together with the results of analysis and simulation. The technique identifies terminals having messages by a process of elimination starting with a poll of groups of terminals. Further, the technique is adaptive in that the sizes of groups to be polled are chosen according to the probability of a terminal having a message. The object of the adaptivity is to minimize the average time required to examine all terminals. The results of analysis and simulation show considerable reduction in this average for systems with many lightly loaded terminals. Moreover, the adaptive feature insures that there is no penalty for heavy loading. With reduced overhead there is a reduction in the average delay of messages.