We focus on aspects of physical distribution of streams, and address the problem of communication reduction for continuous extreme values monitoring over distributed data streams. We firstly develop an effective pruning technique to minimize the number of elements to be kept for extreme values queries. Then we consider the distributed environment, where remote nodes delay the data transmission as late as possible, and adopt the pruning strategy to filter local stream tuples, which is quite efficient in communication reduction. The method is extended to adaptively run in a degraded manner for resource limitation. Analytical analysis and experimental evidences show the efficiency of proposed approach on communication reduction.